Vol. 3, No. 5, 2009

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editors' Addresses Editors' Interests Scientific Advantages Submission Guidelines Submission Form Editorial Login Contacts Author Index To Appear ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print)
Vanishing of trace forms in low characteristics

Appendix: Alexander Premet

Vol. 3 (2009), No. 5, 543–566
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 ${E}_{8}$ over a field of characteristic 5 does not have a “quotient trace form”, answering a question posed in the 1960s.

Keywords
trace form, E8, Richardson's condition, Dynkin index
Mathematical Subject Classification 2000
Primary: 20G05
Secondary: 17B50, 17B25