Simple Lie Algebras over Fields of Positive Characteristic. / Volume 3, : Completion of the Classification / / Helmut Strade.
The problem of classifying the finite-dimensional simple Lie algebras over fields of characteristic p › 0 is a long-standing one. Work on this question during the last 45 years has been directed by the Kostrikin–Shafarevich Conjecture of 1966, which states that over an algebraically closed field of...
Saved in:
Superior document: | Title is part of eBook package: De Gruyter DG Expositions in Mathematics Backlist eBook Package |
---|---|
VerfasserIn: | |
Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2012] ©2013 |
Year of Publication: | 2012 |
Language: | English |
Series: | De Gruyter Expositions in Mathematics ,
57 |
Online Access: | |
Physical Description: | 1 online resource (239 p.) |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
id |
9783110263015 |
---|---|
lccn |
2004043901 |
ctrlnum |
(DE-B1597)172104 (OCoLC)979584872 |
collection |
bib_alma |
record_format |
marc |
spelling |
Strade, Helmut, author. aut http://id.loc.gov/vocabulary/relators/aut Simple Lie Algebras over Fields of Positive Characteristic. Volume 3, Completion of the Classification / Helmut Strade. Berlin ; Boston : De Gruyter, [2012] ©2013 1 online resource (239 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Expositions in Mathematics , 0938-6572 ; 57 Frontmatter -- Contents -- Introduction -- Chapter 16. Miscellaneous -- Chapter 17. Sections -- Chapter 18. Solving the case when T is non-standard -- Chapter 19. Solving the case when all T-roots are solvable -- Chapter 20. Attacking the general case -- Notation -- Bibliography restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star The problem of classifying the finite-dimensional simple Lie algebras over fields of characteristic p › 0 is a long-standing one. Work on this question during the last 45 years has been directed by the Kostrikin–Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p › 5 a finite-dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p › 7 by Block and Wilson in 1988. The generalization of the Kostrikin–Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p › 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block–Wilson–Strade–Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every finite-dimensional simple Lie algebra over an algebraically closed field of characteristic p › 3 is of classical, Cartan, or Melikian type. In the three-volume book, the author is assembling the proof of the Classification Theorem with explanations and references. The goal is a state-of-the-art account on the structure and classification theory of Lie algebras over fields of positive characteristic leading to the forefront of current research in this field. This is the last of three volumes. In this monograph the proof of the Classification Theorem presented in the first volume is concluded. It collects all the important results on the topic which can be found only in scattered scientific literature so far. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) Lie algebras. Gruppentheorie. Lie-Algebra. MATHEMATICS / Algebra / Abstract. bisacsh Field of Positive Characteristic. Lie Algebra. Title is part of eBook package: De Gruyter DG Expositions in Mathematics Backlist eBook Package 9783110494969 ZDB-23-EXM Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 9783110238570 Title is part of eBook package: De Gruyter DGBA Backlist Mathematics 2000-2014 (EN) 9783110238471 Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 9783110637205 ZDB-23-GMA Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2012 9783110288995 ZDB-23-DGG Title is part of eBook package: De Gruyter E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2012 9783110293722 ZDB-23-DMI Title is part of eBook package: De Gruyter E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2012 9783110288926 ZDB-23-DMP print 9783110262988 https://doi.org/10.1515/9783110263015 https://www.degruyter.com/isbn/9783110263015 Cover https://www.degruyter.com/document/cover/isbn/9783110263015/original |
language |
English |
format |
eBook |
author |
Strade, Helmut, Strade, Helmut, |
spellingShingle |
Strade, Helmut, Strade, Helmut, Simple Lie Algebras over Fields of Positive Characteristic. De Gruyter Expositions in Mathematics , Frontmatter -- Contents -- Introduction -- Chapter 16. Miscellaneous -- Chapter 17. Sections -- Chapter 18. Solving the case when T is non-standard -- Chapter 19. Solving the case when all T-roots are solvable -- Chapter 20. Attacking the general case -- Notation -- Bibliography |
author_facet |
Strade, Helmut, Strade, Helmut, |
author_variant |
h s hs h s hs |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Strade, Helmut, |
title |
Simple Lie Algebras over Fields of Positive Characteristic. |
title_full |
Simple Lie Algebras over Fields of Positive Characteristic. Volume 3, Completion of the Classification / Helmut Strade. |
title_fullStr |
Simple Lie Algebras over Fields of Positive Characteristic. Volume 3, Completion of the Classification / Helmut Strade. |
title_full_unstemmed |
Simple Lie Algebras over Fields of Positive Characteristic. Volume 3, Completion of the Classification / Helmut Strade. |
title_auth |
Simple Lie Algebras over Fields of Positive Characteristic. |
title_alt |
Frontmatter -- Contents -- Introduction -- Chapter 16. Miscellaneous -- Chapter 17. Sections -- Chapter 18. Solving the case when T is non-standard -- Chapter 19. Solving the case when all T-roots are solvable -- Chapter 20. Attacking the general case -- Notation -- Bibliography |
title_new |
Simple Lie Algebras over Fields of Positive Characteristic. |
title_sort |
simple lie algebras over fields of positive characteristic. completion of the classification / |
series |
De Gruyter Expositions in Mathematics , |
series2 |
De Gruyter Expositions in Mathematics , |
publisher |
De Gruyter, |
publishDate |
2012 |
physical |
1 online resource (239 p.) Issued also in print. |
contents |
Frontmatter -- Contents -- Introduction -- Chapter 16. Miscellaneous -- Chapter 17. Sections -- Chapter 18. Solving the case when T is non-standard -- Chapter 19. Solving the case when all T-roots are solvable -- Chapter 20. Attacking the general case -- Notation -- Bibliography |
isbn |
9783110263015 9783110494969 9783110238570 9783110238471 9783110637205 9783110288995 9783110293722 9783110288926 9783110262988 |
issn |
0938-6572 ; |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA252 |
callnumber-sort |
QA 3252.3 S78 42004 |
url |
https://doi.org/10.1515/9783110263015 https://www.degruyter.com/isbn/9783110263015 https://www.degruyter.com/document/cover/isbn/9783110263015/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
512 - Algebra |
dewey-full |
512.55 |
dewey-sort |
3512.55 |
dewey-raw |
512.55 |
dewey-search |
512.55 |
doi_str_mv |
10.1515/9783110263015 |
oclc_num |
979584872 |
work_keys_str_mv |
AT stradehelmut simpleliealgebrasoverfieldsofpositivecharacteristicvolume3 |
status_str |
n |
ids_txt_mv |
(DE-B1597)172104 (OCoLC)979584872 |
carrierType_str_mv |
cr |
title_part_txt |
Completion of the Classification / |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter DG Expositions in Mathematics Backlist eBook Package Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 Title is part of eBook package: De Gruyter DGBA Backlist Mathematics 2000-2014 (EN) Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2012 Title is part of eBook package: De Gruyter E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2012 Title is part of eBook package: De Gruyter E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2012 |
is_hierarchy_title |
Simple Lie Algebras over Fields of Positive Characteristic. |
container_title |
Title is part of eBook package: De Gruyter DG Expositions in Mathematics Backlist eBook Package |
_version_ |
1806144285031006208 |
fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>05588nam a22009015i 4500</leader><controlfield tag="001">9783110263015</controlfield><controlfield tag="003">DE-B1597</controlfield><controlfield tag="005">20230228123812.0</controlfield><controlfield tag="006">m|||||o||d||||||||</controlfield><controlfield tag="007">cr || ||||||||</controlfield><controlfield tag="008">230228t20122013gw fo d z eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2004043901</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783110263015</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9783110263015</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-B1597)172104</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)979584872</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-B1597</subfield><subfield code="b">eng</subfield><subfield code="c">DE-B1597</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="050" ind1="0" ind2="0"><subfield code="a">QA252.3</subfield><subfield code="b">.S78 2004</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA252.3</subfield><subfield code="b">.S77 2013</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT002010</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">512.55</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Strade, Helmut, </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Simple Lie Algebras over Fields of Positive Characteristic. </subfield><subfield code="n">Volume 3, </subfield><subfield code="p">Completion of the Classification /</subfield><subfield code="c">Helmut Strade.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin ;</subfield><subfield code="a">Boston : </subfield><subfield code="b">De Gruyter, </subfield><subfield code="c">[2012]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">©2013</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (239 p.)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="347" ind1=" " ind2=" "><subfield code="a">text file</subfield><subfield code="b">PDF</subfield><subfield code="2">rda</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">De Gruyter Expositions in Mathematics ,</subfield><subfield code="x">0938-6572 ;</subfield><subfield code="v">57</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="t">Frontmatter -- </subfield><subfield code="t">Contents -- </subfield><subfield code="t">Introduction -- </subfield><subfield code="t">Chapter 16. Miscellaneous -- </subfield><subfield code="t">Chapter 17. Sections -- </subfield><subfield code="t">Chapter 18. Solving the case when T is non-standard -- </subfield><subfield code="t">Chapter 19. Solving the case when all T-roots are solvable -- </subfield><subfield code="t">Chapter 20. Attacking the general case -- </subfield><subfield code="t">Notation -- </subfield><subfield code="t">Bibliography</subfield></datafield><datafield tag="506" ind1="0" ind2=" "><subfield code="a">restricted access</subfield><subfield code="u">http://purl.org/coar/access_right/c_16ec</subfield><subfield code="f">online access with authorization</subfield><subfield code="2">star</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The problem of classifying the finite-dimensional simple Lie algebras over fields of characteristic p › 0 is a long-standing one. Work on this question during the last 45 years has been directed by the Kostrikin–Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p › 5 a finite-dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p › 7 by Block and Wilson in 1988. The generalization of the Kostrikin–Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p › 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block–Wilson–Strade–Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every finite-dimensional simple Lie algebra over an algebraically closed field of characteristic p › 3 is of classical, Cartan, or Melikian type. In the three-volume book, the author is assembling the proof of the Classification Theorem with explanations and references. The goal is a state-of-the-art account on the structure and classification theory of Lie algebras over fields of positive characteristic leading to the forefront of current research in this field. This is the last of three volumes. In this monograph the proof of the Classification Theorem presented in the first volume is concluded. It collects all the important results on the topic which can be found only in scattered scientific literature so far.</subfield></datafield><datafield tag="530" ind1=" " ind2=" "><subfield code="a">Issued also in print.</subfield></datafield><datafield tag="538" ind1=" " ind2=" "><subfield code="a">Mode of access: Internet via World Wide Web.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023)</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Lie algebras.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Gruppentheorie.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lie-Algebra.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Algebra / Abstract.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Field of Positive Characteristic.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Lie Algebra.</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">DG Expositions in Mathematics Backlist eBook Package</subfield><subfield code="z">9783110494969</subfield><subfield code="o">ZDB-23-EXM</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">DGBA Backlist Complete English Language 2000-2014 PART1</subfield><subfield code="z">9783110238570</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">DGBA Backlist Mathematics 2000-2014 (EN)</subfield><subfield code="z">9783110238471</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">DGBA Mathematics - 2000 - 2014</subfield><subfield code="z">9783110637205</subfield><subfield code="o">ZDB-23-GMA</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2012</subfield><subfield code="z">9783110288995</subfield><subfield code="o">ZDB-23-DGG</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2012</subfield><subfield code="z">9783110293722</subfield><subfield code="o">ZDB-23-DMI</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2012</subfield><subfield code="z">9783110288926</subfield><subfield code="o">ZDB-23-DMP</subfield></datafield><datafield tag="776" ind1="0" ind2=" "><subfield code="c">print</subfield><subfield code="z">9783110262988</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9783110263015</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://www.degruyter.com/isbn/9783110263015</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="3">Cover</subfield><subfield code="u">https://www.degruyter.com/document/cover/isbn/9783110263015/original</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">978-3-11-023847-1 DGBA Backlist Mathematics 2000-2014 (EN)</subfield><subfield code="c">2000</subfield><subfield code="d">2014</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">978-3-11-023857-0 DGBA Backlist Complete English Language 2000-2014 PART1</subfield><subfield code="c">2000</subfield><subfield code="d">2014</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_BACKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_CL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_DGALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EBACKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ECL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EEBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ESTMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_STMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV-deGruyter-alles</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA12STME</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA13ENGE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA18STMEE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA5EBK</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-DGG</subfield><subfield code="b">2012</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-DMI</subfield><subfield code="b">2012</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-DMP</subfield><subfield code="b">2012</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-EXM</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-GMA</subfield><subfield code="c">2000</subfield><subfield code="d">2014</subfield></datafield></record></collection> |