New simple modular Lie superalgebras as generalized prolongs

S. Bouarroudj; P. Ya Grozman; D. A. Leites

doi:10.1007/s10688-008-0025-3

New simple modular Lie superalgebras as generalized prolongs

S. Bouarroudj, P. Ya Grozman, D. A. Leites

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Over algebraically closed fields of characteristic p > 2, -prolongations of simple finite dimensional Lie algebras and Lie superalgebras with Cartan matrix are studied for certain simplest gradings of these algebras. We discover several new simple Lie superalgebras, serial and exceptional, including super versions of Brown and Melikyan algebras, and thus corroborate the super analog of the Kostrikin-Shafarevich conjecture. Simple Lie superalgebras with 2 × 2 Cartan matrices are classified.

Original language	English (US)
Pages (from-to)	161-168
Number of pages	8
Journal	Functional Analysis and Its Applications
Volume	42
Issue number	3
DOIs	https://doi.org/10.1007/s10688-008-0025-3
State	Published - Jul 2008

Keywords

Cartan prolong
Lie superalgebra

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1007/s10688-008-0025-3

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AU - Leites, D. A.

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N2 - Over algebraically closed fields of characteristic p > 2, -prolongations of simple finite dimensional Lie algebras and Lie superalgebras with Cartan matrix are studied for certain simplest gradings of these algebras. We discover several new simple Lie superalgebras, serial and exceptional, including super versions of Brown and Melikyan algebras, and thus corroborate the super analog of the Kostrikin-Shafarevich conjecture. Simple Lie superalgebras with 2 × 2 Cartan matrices are classified.

AB - Over algebraically closed fields of characteristic p > 2, -prolongations of simple finite dimensional Lie algebras and Lie superalgebras with Cartan matrix are studied for certain simplest gradings of these algebras. We discover several new simple Lie superalgebras, serial and exceptional, including super versions of Brown and Melikyan algebras, and thus corroborate the super analog of the Kostrikin-Shafarevich conjecture. Simple Lie superalgebras with 2 × 2 Cartan matrices are classified.

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KW - Lie superalgebra

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New simple modular Lie superalgebras as generalized prolongs

Abstract

Keywords

ASJC Scopus subject areas

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