Inner products of 2-representations

Nora Ganter

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arXiv · 1110.1711

Inner products of 2-representations

Nora Ganter

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Abstract

We define and calculate inner products of 2-representations. Along the way, we prove that the categorical trace Tr(-) of [Ganter and Kapranov, Representation and character theory in 2-categories, Sec. 3] is multiplicative with respect to various notions of categorical tensor product, and we identify the center of the category V^G of [loc. cit., Sec. 4.2]. We discuss applications, ranging from Schur's result about the number of projective representations to a formula for the Hochschild cohomology of a global quotient orbifold.

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Nora Ganter. 2012-08-24. Inner products of 2-representations. https://arxiv.org/abs/1110.1711

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