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Submission: 2008, May 29

A finite-dimensional representation of an algebraic group G gives a trace symmetric bilinear form on the Lie algebra of G. We give a criterion in terms of the root system data for this form to vanish. 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.

2000 Mathematics Subject Classification: 20G05 (17B50; 17B25)

Keywords and Phrases: trace forms, quotient trace forms, E8, Dynkin index

Full text: dvi.gz 34 k, dvi 71 k, ps.gz 952 k, pdf.gz 185 k, pdf 210 k.

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