Manchester Algebra Seminar - Jay Taylor - University of Manchester
|Dates:||11 May 2021|
|Times:||13:00 - 14:00|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
|Who is it for:||University staff, Current University students|
Speaker: Adam Thomas - University of Warwick
Speaker: Jay Taylor - University of Manchester
Title: Invariant Bilinear Forms on Lie Algebras
Abstract: Assume a group G acts linearly on a k-vector space V. Then G acts on the space of bilinear forms on V. A standard question in representation theory asks whether G fixes a nondegenerate bilinear form on V. Equivalently, is there a G-equivariant isomorphism between V and its dual module Hom(V,k).
In this talk we consider the case where G is a connected reductive algebraic k-group acting on its Lie algebra V = Lie(G) via the adjoint representation. A result of Herpel strongly suggests that V should admit a non-degenerate G-invariant bilinear form whenever the characteristic of k is ‘pretty good’ for G. In this talk we discuss some recent work on this problem and explain some of the standard consequences of this result, due to Richardson.
Travel and Contact Information
Zoom - online
Alan Turing Building