Mathematics > Representation Theory
[Submitted on 21 Dec 2007 (v1), last revised 6 Apr 2009 (this version, v4)]
Title:Vanishing of trace forms in low characteristics
View PDFAbstract: Every finite-dimensional representation of an algebraic group G gives a trace symmetric bilinear form on the Lie algebra of G. We give criteria in terms of root system data for the existence of a representation such that this form is nonzero or nondegenerate. As a corollary, we show that a Lie algebra of type E8 over a field of characteristic 5 does not have a so-called "quotient trace form", answering a question posed in the 1960s.
Submission history
From: Skip Garibaldi [view email][v1] Fri, 21 Dec 2007 18:10:34 UTC (9 KB)
[v2] Thu, 29 May 2008 16:58:56 UTC (20 KB)
[v3] Wed, 15 Oct 2008 13:42:02 UTC (26 KB)
[v4] Mon, 6 Apr 2009 19:55:59 UTC (28 KB)
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