This article is cited in 12 papers

New Simple Modular Lie Superalgebras as Generalized Prolongs

S. Bouarroudj^a, P. Ya. Grozman^b, D. A. Leites<sup>b

a</sup> United Arab Emirates University
^b Stockholm University

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 $2\times 2$ Cartan matrices are classified.

Keywords: Cartan prolong, Lie superalgebra.

UDC: 512.554.38

Received: 09.12.2006

DOI: 10.4213/faa2924

 English version: Functional Analysis and Its Applications, 2008, 42:3, 161–168

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