Premonoidal categories associated with representations of finite groups and their quantum doubles

Details Premonoidal categories associated with representations of finite groups and their quantum doubles Premonoidal categories associated with representations of finite groups and their quantum doubles

2006-06-28

arxiv.org/abs/math/0606704v1

Mathematics

Category Theory

Scientific paper

We study the construction of premonoidal categories, where the pentagon relation fails, through representations of finite group algebras and their quantum doubles. Both finite group algebras and their quantum doubles have a finite number of irreducible representations. We show that in each case there are at least $2^{n-1}$ inequivalent premonoidal categories of representations, where $n$ is the number of irreducible representations. By construction, for the case of finite group algebras the categories are symmetric whereas for the quantum doubles the categories are braided.

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