Vanishing of trace forms in low characteristics
Representation Theory
2010-02-17 v4
Abstract
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.
Cite
@article{arxiv.0712.3764,
title = {Vanishing of trace forms in low characteristics},
author = {Skip Garibaldi and Alexander Premet},
journal= {arXiv preprint arXiv:0712.3764},
year = {2010}
}
Comments
Slightly revised since v3. Added short section 8 on Richardson's condition