Simple Lie Algebras over Fields of Positive Characteristic. / Volume I, : Structure Theory / / 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...
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2008] ©2004 |
Year of Publication: | 2008 |
Edition: | Reprint 2014 |
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Strade, Helmut, author. aut http://id.loc.gov/vocabulary/relators/aut Simple Lie Algebras over Fields of Positive Characteristic. Volume I, Structure Theory / Helmut Strade. Reprint 2014 Berlin ; Boston : De Gruyter, [2008] ©2004 1 online resource (540 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Expositions in Mathematics , 0938-6572 ; 38 Frontmatter -- Contents -- Introduction -- Chapter 1. Toral subalgebras in p-envelopes -- Chapter 2. Lie algebras of special -- derivations -- Chapter 3. Derivation simple algebras and -- modules -- Chapter 4. Simple Lie algebras -- Chapter 5. Recognition theorems -- Chapter 6. The isomorphism problem -- Chapter 7. Structure of simple Lie algebras -- Chapter 8. Pairings of induced modules -- Chapter 9. Toral rank 1 Lie algebras -- Backmatter 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 first volume is devoted to preparing the ground for the classification work to be performed in the second and third volume. The concise presentation of the general theory underlying the subject matter and the presentation of classification results on a subclass of the simple Lie algebras for all odd primes make this volume an invaluable source and reference for all research mathematicians and advanced graduate students in albegra. 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. Einfache Lie-Algebra. Lie-Algebra. Positive Charakteristik. MATHEMATICS / Algebra / Abstract. bisacsh Lie Algebra, Fields of Positive Characteristic, Structure Theory. 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 2008 9783110212129 ZDB-23-DGG Title is part of eBook package: De Gruyter E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2008 9783110212136 Title is part of eBook package: De Gruyter E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2008 9783110209082 ZDB-23-DMN print 9783110142112 https://doi.org/10.1515/9783110197945 https://www.degruyter.com/isbn/9783110197945 Cover https://www.degruyter.com/document/cover/isbn/9783110197945/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 1. Toral subalgebras in p-envelopes -- Chapter 2. Lie algebras of special -- derivations -- Chapter 3. Derivation simple algebras and -- modules -- Chapter 4. Simple Lie algebras -- Chapter 5. Recognition theorems -- Chapter 6. The isomorphism problem -- Chapter 7. Structure of simple Lie algebras -- Chapter 8. Pairings of induced modules -- Chapter 9. Toral rank 1 Lie algebras -- Backmatter |
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 I, Structure Theory / Helmut Strade. |
title_fullStr |
Simple Lie Algebras over Fields of Positive Characteristic. Volume I, Structure Theory / Helmut Strade. |
title_full_unstemmed |
Simple Lie Algebras over Fields of Positive Characteristic. Volume I, Structure Theory / Helmut Strade. |
title_auth |
Simple Lie Algebras over Fields of Positive Characteristic. |
title_alt |
Frontmatter -- Contents -- Introduction -- Chapter 1. Toral subalgebras in p-envelopes -- Chapter 2. Lie algebras of special -- derivations -- Chapter 3. Derivation simple algebras and -- modules -- Chapter 4. Simple Lie algebras -- Chapter 5. Recognition theorems -- Chapter 6. The isomorphism problem -- Chapter 7. Structure of simple Lie algebras -- Chapter 8. Pairings of induced modules -- Chapter 9. Toral rank 1 Lie algebras -- Backmatter |
title_new |
Simple Lie Algebras over Fields of Positive Characteristic. |
title_sort |
simple lie algebras over fields of positive characteristic. structure theory / |
series |
De Gruyter Expositions in Mathematics , |
series2 |
De Gruyter Expositions in Mathematics , |
publisher |
De Gruyter, |
publishDate |
2008 |
physical |
1 online resource (540 p.) Issued also in print. |
edition |
Reprint 2014 |
contents |
Frontmatter -- Contents -- Introduction -- Chapter 1. Toral subalgebras in p-envelopes -- Chapter 2. Lie algebras of special -- derivations -- Chapter 3. Derivation simple algebras and -- modules -- Chapter 4. Simple Lie algebras -- Chapter 5. Recognition theorems -- Chapter 6. The isomorphism problem -- Chapter 7. Structure of simple Lie algebras -- Chapter 8. Pairings of induced modules -- Chapter 9. Toral rank 1 Lie algebras -- Backmatter |
isbn |
9783110197945 9783110494969 9783110238570 9783110238471 9783110637205 9783110212129 9783110212136 9783110209082 9783110142112 |
issn |
0938-6572 ; |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA252 |
callnumber-sort |
QA 3252.3 S78 EB VOL 11 |
url |
https://doi.org/10.1515/9783110197945 https://www.degruyter.com/isbn/9783110197945 https://www.degruyter.com/document/cover/isbn/9783110197945/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
512 - Algebra |
dewey-full |
512/.55 |
dewey-sort |
3512 255 |
dewey-raw |
512/.55 |
dewey-search |
512/.55 |
doi_str_mv |
10.1515/9783110197945 |
oclc_num |
979581845 |
work_keys_str_mv |
AT stradehelmut simpleliealgebrasoverfieldsofpositivecharacteristicvolumei |
status_str |
n |
ids_txt_mv |
(DE-B1597)32307 (OCoLC)979581845 |
carrierType_str_mv |
cr |
title_part_txt |
Structure Theory / |
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 2008 Title is part of eBook package: De Gruyter E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2008 Title is part of eBook package: De Gruyter E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2008 |
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 |
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1806144224030097408 |
fullrecord |
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