138 research outputs found

    Classifying braidings on fusion categories

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    We show that braidings on a fusion category C\mathcal{C} correspond to certain fusion subcategories of the center of C\mathcal{C} transversal to the canonical Lagrangian algebra. This allows to classify braidings on non-degenerate and group-theoretical fusion categories.Comment: 14 pages, minor corrections, new references adde

    Hopf algebra actions on strongly separable extensions of depth two

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    We bring together ideas in analysis of Hopf *-algebra actions on II_1 subfactors of finite Jones index and algebraic characterizations of Frobenius, Galois and cleft Hopf extensions to prove a non-commutative algebraic analogue of the classical theorem: a finite field extension is Galois iff it is separable and normal. Suppose N < M is a separable Frobenius extension of k-algebras split as N-bimodules with a trivial centralizer C_M(N). Let M_1 := End(M)_N and M_2 := End(M_1)_M be the endomorphism algebras in the Jones tower N < M < M_1 < M_2. We show that under depth 2 conditions on the second centralizers A := C_{M_1}(N) and B : = C_{M_2}(M) the algebras A and B are semisimple Hopf algebras dual to one another and such that M_1 is a smash product of M and A, and that M is a B-Galois extension of N.Comment: 21 pages, ams-latex; to appear in Advances in Mathematic

    Autoequivalences of tensor categories attached to quantum groups at roots of 11

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    We compute the group of braided tensor autoequivalences and the Brauer-Picard group of the representation category of the small quantum group uq(g)\mathfrak{u}_q(\mathfrak{g}), where qq is a root of unity.Comment: 29 pages, late