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.
"Vanishing of trace forms in low characteristics." Algebra Number Theory 3 (5) 543 - 566, 2009. https://doi.org/10.2140/ant.2009.3.543