Preprint 79/2006

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

Alexei Lebedev

Contact the author: Please use for correspondence this email.
Submission date: 22. Aug. 2006
Pages: 33
Bibtex
MSC-Numbers: 17B60
Keywords and phrases: Lie algebras, Lie superalgebras
Download full preprint: PDF (354 kB), PS ziped (290 kB)

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.

07.06.2018, 02:11