Algebra & Number Theory
- Algebra Number Theory
- Volume 3, Number 5 (2009), 543-566.
Vanishing of trace forms in low characteristics
Every finite-dimensional representation of an algebraic group gives a trace symmetric bilinear form on the Lie algebra of . 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 over a field of characteristic 5 does not have a “quotient trace form”, answering a question posed in the 1960s.
Algebra Number Theory, Volume 3, Number 5 (2009), 543-566.
Received: 16 July 2008
Revised: 5 March 2009
Accepted: 6 April 2009
First available in Project Euclid: 20 December 2017
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Garibaldi, Skip. Vanishing of trace forms in low characteristics. Algebra Number Theory 3 (2009), no. 5, 543--566. doi:10.2140/ant.2009.3.543. https://projecteuclid.org/euclid.ant/1513797448