Open Access
Translator Disclaimer
2009 Vanishing of trace forms in low characteristics
Skip Garibaldi
Algebra Number Theory 3(5): 543-566 (2009). DOI: 10.2140/ant.2009.3.543

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 “quotient trace form”, answering a question posed in the 1960s.

Citation

Download Citation

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

Information

Received: 16 July 2008; Revised: 5 March 2009; Accepted: 6 April 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1282.20052
MathSciNet: MR2578888
Digital Object Identifier: 10.2140/ant.2009.3.543

Subjects:
Primary: 20G05
Secondary: 17B25 , 17B50

Keywords: Dynkin index , E8 , Richardson's condition , trace form

Rights: Copyright © 2009 Mathematical Sciences Publishers

JOURNAL ARTICLE
24 PAGES


SHARE
Vol.3 • No. 5 • 2009
MSP
Back to Top