Representation motives, a cautionary tale

Lieven Le Bruyn (University of Antwerp)

Wednesday 13th March 16:00-17:00 Maths 311B

Abstract

Principal GL(n)-bundles (aka vector bundles) are locally trivial in the Zariski topology, whereas principal PGL(n)-bundles (aka Azumaya algebras) are not, to the delight of every non-commutative algebraist. Still, this makes the calculation of motives of representation schemes of algebras next to impossible. In very special cases, Brauer-Severi schemes (and their motives) can be used to approach this problem inductively. We illustrate this in the case of super-potential algebras.

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