Virtual representation motives

2019/04/29 by Bruyn, Lieven Le
#FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1904.12536

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 tackle this problem inductively. We illustrate this in the case of certain superpotential algebras.

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