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New simple modular Lie superalgebras as generalized prolongs. (English) Zbl 1160.17012

Funct. Anal. Appl. 42, No. 3, 161-168 (2008); translation from Funkts. Anal. Prilozh. 42, No. 3, 1-9 (2008).
Summary: 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 \(2 \times 2\) Cartan matrices are classified.

MSC:

17B50 Modular Lie (super)algebras
17B65 Infinite-dimensional Lie (super)algebras

Software:

SuperLie
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Full Text: DOI arXiv

References:

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