

Preprint 79/2006
Non-degenerate bilinear forms in characteristic 2, related contact forms, simple Lie algebras and superalgebras
Alexei Lebedev
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Submission date: 22. Aug. 2006
Pages: 33
Bibtex
MSC-Numbers: 17B60
Keywords and phrases: Lie algebras, Lie superalgebras
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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.