منابع مشابه
Correspondences of Ribbon Categories
Much of algebra and representation theory can be formulated in the general framework of tensor categories. The aim of this paper is to further develop this theory for braided tensor categories. Several results are established that do not have a substantial counterpart for symmetric tensor categories. In particular, we exhibit various equivalences involving categories of modules over algebras in...
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The RSK correspondence generalises the Robinson-Schensted correspondence by replacing permutation matrices by matrices with entries in N, and standard Young tableaux by semistandard ones. For r ∈ N>0, the Robinson-Schensted correspondence can be trivially extended, using the r-quotient map, to one between r-coloured permutations and pairs of standard r-ribbon tableaux built on a fixed r-core (t...
متن کاملQuantum Groups and Ribbon G-categories
For a group G, the notion of a ribbon G-category was introduced in [Tu4] with a view towards constructing 3-dimensional homotopy quantum field theories (HQFT's) with target K(G, 1). We discuss here how to derive ribbon G-categories from a simple complex Lie algebra g where G is the center of g. Our construction is based on a study of representations of the quantum group U q (g) at a root of uni...
متن کاملRibbon structure in symmetric pre-monoidal categories
Let U(g) denote the universal enveloping algebra of a Lie algebra g. We show the existence of a ribbon algebra structure in a particular deformation of U(g) which leads to a symmetric pre-monoidal category of U(g)-modules.
متن کاملOn a Family of Non-unitarizable Ribbon Categories
We consider several families of categories. The first are quotients of Andersen’s tilting module categories for quantum groups of Lie type B at odd roots of unity. The second consists of categories of type BC constructed from idempotents in BMW -algebras. Our main result is to show that these families coincide as braided tensor categories using a recent theorem of Tuba and Wenzl. By appealing t...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2006
ISSN: 0001-8708
DOI: 10.1016/j.aim.2005.04.007