Module categories over the Drinfeld double of a finite group

By V. Ostrik. 2002

234 citations recorded by the source corpus.

. We classify the module categories over the double (possibly twisted) of a ﬁnite group.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9fe3442dd6207146429cfa6722bbc85bc167a8de

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Citations in the corpus

Frobenius–Schur indicators and exponents of spherical categories (2005, background): “We also study an important class of quasi-Hopf algebras, namely the group-theoretical quasi-Hopf algebras corresponding to the group-theoretical fusion categories introduced by Ostrik [ Ost03 ].”
WEAKLY GROUP-THEORETICAL AND SOLVABLE FUSION CATEGORIES (2008, background): “Consider the fusion category C = VecG,!,K, of (K, )-biequivariant (G,!)-graded vector spaces (see [O1, O2 ]).”
A Finiteness Property for Braided Fusion Categories (2009, background): “By a “powerful” quantum computer we mean universal and the corresponding (classical) computational complexity class is”
On tensor categories attached to cells in affine Weyl groups, III (2000, background): “Recall that the pro-algebraic group Aut(O) of automorpshisms of O acts on fl. The multiplicative group (“loop rotations”) Gm is contained in Aut(O), and acts on f”
Q-system completion for C⁎ 2-categories (2021, unknown): “By [Ost03b, Thm. 3.1], an irreducible Q-system in Hilb fd ( G, ω ) is given by a pair ( H, µ ) where H ≤ G and µ : H × H → U (1) satisfies dµ = ω | H .”
Categorical Morita Equivalence for Group-Theoretical Categories (2006, background): “It was shown in Ostrik (2003b) that if the tensor categories and are weakly Morita equivalent, then their Drinfeld centers are equivalent as braided tensor categories.”
Tensor categories: a selective guided tour (2008, background): “• Algebras in and module categories over the category Ck(G,ω) defined in Section 1 were studied in [223].”
Non-group-theoretical semisimple Hopf algebras from group actions on fusion categories (2007, methodology): “Below we recall a description of group-theoretical categories from [21].”
Orbifold groupoids (2020, background): “Irreducible boundary conditions turn out to be classified precisely by the (H, ν2) data, so no exotic orbifolds are available [16, 17].”
On fusion categories (2002, unknown): “It is clear from the results of [ O1 ] that the class of group-theoretical categories is closed under tensor product, taking the opposite category, and taking the dual category with respect to an indecomposable module category.”
On module categories over finite-dimensional Hopf algebras (2006, methodology): “Thus, if M is simple then End(M) has no non-zero right ideals. Example 1.16. [Z], [ O1 , Prop.”
Anyon condensation and tensor categories (2013, background): “This set can be characterized by a pair (H, ω), where H is a subgroup and ω ∈H 2(H, C×) [63].”