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arXiv · 1904.12536

Virtual representation motives

Lieven Le Bruyn
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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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Lieven Le Bruyn. 2019-04-29. Virtual representation motives. https://arxiv.org/abs/1904.12536

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