Inner products of 2-representations
Advances in Mathematics | ACADEMIC PRESS INC ELSEVIER SCIENCE | Published : 2015
We define and calculate inner products of 2-representations. Along the way, we prove that the categorical trace Tr(-) of [24, Sec. 3] is multiplicative with respect to various notions of categorical tensor product, and we identify the center of the category of equivariant objects. We discuss applications, ranging from Schur's result about the number of irreducible projective representations to a formula for the Hochschild cohomology of a global quotient orbifold.
Awarded by NSF
Ganter was supported by NSF-grant DMS-0504539 and by a Centenary Fellowship by the Faculty of Science at the University of Melbourne. Work on this project began while Canter was at Colby College, Maine.