# Manchester Algebra Seminar - Jay Taylor - University of Manchester

Dates: | 11 May 2021 |
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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.

Time: 1pm Place: Zoom