Simple Lie Algebras over Fields of Positive Characteristic. / Volume II, : Classifying the Absolute Toral Rank Two Case / / 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, , [2009] ©2009 |
Year of Publication: | 2009 |
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Strade, Helmut, author. aut http://id.loc.gov/vocabulary/relators/aut Simple Lie Algebras over Fields of Positive Characteristic. Volume II, Classifying the Absolute Toral Rank Two Case / Helmut Strade. Berlin ; Boston : De Gruyter, [2009] ©2009 1 online resource (385 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Expositions in Mathematics , 0938-6572 ; 42 Frontmatter -- Contents -- Introduction -- Chapter 10. Tori in Hamiltonian and Melikian algebras -- Chapter 11. 1-sections -- Chapter 12. Sandwich elements and rigid tori -- Chapter 13. Towards graded algebras -- Chapter 14. The toral rank 2 case -- Chapter 15. Supplements to Volume 1 -- 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 is the second part of the three-volume book about the classification of the simple Lie algebras over algebraically closed fields of characteristics › 3. The first volume contains the methods, examples, and a first classification result. This second volume presents insight in the structure of tori of Hamiltonian and Melikian algebras. Based on sandwich element methods due to Aleksei. I. Kostrikin and Alexander A. Premet and the investigation of absolute toral rank 2 simple Lie algebras over algebraically closed fields of characteristics › 3 is given. 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 Lie Algebra, Field of Positive Characteristic, Absolute Toral Rank Two Case. 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 2009 9783110219517 ZDB-23-DGG Title is part of eBook package: De Gruyter E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2009 9783110219524 Title is part of eBook package: De Gruyter E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2009 9783110219463 ZDB-23-DMN print 9783110197013 https://doi.org/10.1515/9783110203059 https://www.degruyter.com/isbn/9783110203059 Cover https://www.degruyter.com/document/cover/isbn/9783110203059/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 10. Tori in Hamiltonian and Melikian algebras -- Chapter 11. 1-sections -- Chapter 12. Sandwich elements and rigid tori -- Chapter 13. Towards graded algebras -- Chapter 14. The toral rank 2 case -- Chapter 15. Supplements to Volume 1 -- 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 II, Classifying the Absolute Toral Rank Two Case / Helmut Strade. |
title_fullStr |
Simple Lie Algebras over Fields of Positive Characteristic. Volume II, Classifying the Absolute Toral Rank Two Case / Helmut Strade. |
title_full_unstemmed |
Simple Lie Algebras over Fields of Positive Characteristic. Volume II, Classifying the Absolute Toral Rank Two Case / Helmut Strade. |
title_auth |
Simple Lie Algebras over Fields of Positive Characteristic. |
title_alt |
Frontmatter -- Contents -- Introduction -- Chapter 10. Tori in Hamiltonian and Melikian algebras -- Chapter 11. 1-sections -- Chapter 12. Sandwich elements and rigid tori -- Chapter 13. Towards graded algebras -- Chapter 14. The toral rank 2 case -- Chapter 15. Supplements to Volume 1 -- Backmatter |
title_new |
Simple Lie Algebras over Fields of Positive Characteristic. |
title_sort |
simple lie algebras over fields of positive characteristic. classifying the absolute toral rank two case / |
series |
De Gruyter Expositions in Mathematics , |
series2 |
De Gruyter Expositions in Mathematics , |
publisher |
De Gruyter, |
publishDate |
2009 |
physical |
1 online resource (385 p.) Issued also in print. |
contents |
Frontmatter -- Contents -- Introduction -- Chapter 10. Tori in Hamiltonian and Melikian algebras -- Chapter 11. 1-sections -- Chapter 12. Sandwich elements and rigid tori -- Chapter 13. Towards graded algebras -- Chapter 14. The toral rank 2 case -- Chapter 15. Supplements to Volume 1 -- Backmatter |
isbn |
9783110203059 9783110494969 9783110238570 9783110238471 9783110637205 9783110219517 9783110219524 9783110219463 9783110197013 |
issn |
0938-6572 ; |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA252 |
callnumber-sort |
QA 3252.3 |
url |
https://doi.org/10.1515/9783110203059 https://www.degruyter.com/isbn/9783110203059 https://www.degruyter.com/document/cover/isbn/9783110203059/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
510 - Mathematics |
dewey-full |
510 |
dewey-sort |
3510 |
dewey-raw |
510 |
dewey-search |
510 |
doi_str_mv |
10.1515/9783110203059 |
oclc_num |
719449634 |
work_keys_str_mv |
AT stradehelmut simpleliealgebrasoverfieldsofpositivecharacteristicvolumeii |
status_str |
n |
ids_txt_mv |
(DE-B1597)33380 (OCoLC)719449634 |
carrierType_str_mv |
cr |
title_part_txt |
Classifying the Absolute Toral Rank Two Case / |
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 2009 Title is part of eBook package: De Gruyter E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2009 Title is part of eBook package: De Gruyter E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2009 |
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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1770177436575596544 |
fullrecord |
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