Equivariant Modular Categories via Dijkgraaf-Witten Theory

Details Equivariant Modular Categories via Dijkgraaf-Witten Theory Equivariant Modular Categories via Dijkgraaf-Witten Theory

2011-03-15

arxiv.org/abs/1103.2963v3

Mathematics

Quantum Algebra

52 pages, 3 figures, v2: typos corrected, v3: conventions concerning left and right actions fixed (mainly section 4)

Scientific paper

Based on a weak action of a finite group J on a finite group G, we present a geometric construction of J-equivariant Dijkgraaf-Witten theory as an extended topological field theory. The construction yields an explicitly accessible class of equivariant modular tensor categories. For the action of a group J on a group G, the category is described as the representation category of a J-ribbon algebra that generalizes the Drinfel'd double of the finite group G.

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