Non-degenerate bilinear forms in characteristic 2, related contact forms, simple Lie algebras and superalgebras

2006/01/22 by Alexei Lebedev, Lebedev, Alexei
Mathematics · #17B60 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:17B60

paper · pdf · doi:10.48550/arxiv.math/0601536

Minor corrections in the definitions have been made

openalex publication_date 2006/01/22 · arxiv created 2006/09/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Non-degenerate bilinear forms over fields of characteristic 2, in particular, non-symmetric ones, are classified with respect to various equivalences, and the Lie algebras preserving them are described. Although it is known that there are two series of distinct finite simple Chevalley groups preserving the non-degenerate symmetric bilinear forms on the space of even dimension, the description of simple Lie algebras related to the ones that preserve these forms is new. The classification of 1-forms is shown to be related to one of the considered equivalences of bilinear forms. A version of the above results for superspaces is also given.

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