Structure Theory.
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 has been directed by the Kostrikin-Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p> 5...
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin/Boston :
De Gruyter,
2017
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| Edition: | 2nd ed. |
| Series: | De Gruyter expositions in mathematics.
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| Subjects: | |
| Local Note: | ProQuest Ebook Central |
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| 100 | 1 | |a Strade, Helmut. | |
| 245 | 1 | 0 | |a Structure Theory. |
| 250 | |a 2nd ed. | ||
| 260 | |a Berlin/Boston : |b De Gruyter, |c 2017. | ||
| 300 | |a 1 online resource (550 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 490 | 1 | |a De Gruyter Expositions in Mathematics ; |v v. 38 | |
| 500 | |a 6.5 Hamiltonian algebras. | ||
| 505 | 0 | |a Introduction ; 1. Toral subalgebras in p-envelopes ; 1.1 p-envelopes ; 1.2 The absolute toral rank ; 1.3 Extended roots ; 1.4 Absolute toral ranks of parametrized families ; 1.5 Toral switching ; 2. Lie algebras of special derivations ; 2.1 Divided power mappings. | |
| 505 | 8 | |a 2.2 Subalgebras defined by flags 2.3 Transitive embeddings of Lie algebras ; 2.4 Automorphisms and derivations ; 2.5 Filtrations and gradations ; 2.6 Minimal embeddings of filtered and associated graded Lie algebras ; 2.7 Miscellaneous ; 2.8 A universal embedding. | |
| 505 | 8 | |a 2.9 The constructions can be made basis free 3. Derivation simple algebras and modules ; 3.1 Frobenius extensions ; 3.2 Induced modules ; 3.3 Block's theorems ; 3.4 Derivation semisimple associative algebras ; 3.5 Weisfeiler's theorems ; 3.6 Conjugacy classes of tori. | |
| 505 | 8 | |a 4. Simple Lie algebras 4.1 Classical Lie algebras ; 4.2 Lie algebras of Cartan type ; 4.3 Melikian algebras ; 4.4 Simple Lie algebras in characteristic 3 ; 5. Recognition theorems ; 5.1 Cohomology groups ; 5.2 From local to global Lie algebras ; 5.3 Representations. | |
| 505 | 8 | |a 5.4 Generating Melikian algebras 5.5 TheWeak Recognition Theorem ; 5.6 The Recognition Theorem ; 5.7 Wilson's Theorem ; 6. The isomorphism problem ; 6.1 A first attack ; 6.2 The compatibility property ; 6.3 Special algebras ; 6.4 Orbits of Hamiltonian forms. | |
| 520 | |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 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 simple 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. This first volume is devoted to preparing the ground for the classification work to be performed in the second and third volumes. 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 will make this volume an invaluable source and reference for all research mathematicians and advanced graduate students in algebra. The second edition is corrected. Contents Toral subalgebras in p-envelopes Lie algebras of special derivations Derivation simple algebras and modules Simple Lie algebras Recognition theorems The isomorphism problem Structure of simple Lie algebras Pairings of induced modules Toral rank 1 Lie algebras. | ||
| 546 | |a In English. | ||
| 588 | 0 | |a Print version record. | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Lie algebras. | |
| 758 | |i has work: |a Structure theory (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGmKWhT9BchFyWWCRbpv6q |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Strade, Helmut. |t Structure Theory. |d Berlin/Boston : De Gruyter, ©2017 |z 9783110515169 |
| 830 | 0 | |a De Gruyter expositions in mathematics. | |
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