Dr. Sonia Natale
Affil.: Facultad de Matematica, Astronomia y Fisica,
Universidad Nacional de Cordoba. CIEM -- CONICET. (5000)
Ciudad Universitaria, Cordoba, Argentina
Tensor categories attached to double groupoids
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Abstract. This is joint work with Nicolas Andruskiewitsch, available at http://www.arxiv.org/abs/math.QA/0408045. We present the construction of a quantum groupoid structure in the span of the boxes in a double groupoid satisfying a natural filling condition, by introducing a certain perturbation in (any) one of the groupoid algebra structures. This is achieved by considering a family of 'corner' functions defined on a double groupoid. In fact, the perturbation is done for a more general class of functions. This extends previous work on the vacant case that appeared in math.QA/0308228. Several important classes of examples of tensor categories are shown to fit into this construction.
Certain invariants such as a pivotal group-like element and quantum and Frobenius-Perron dimensions of simple objects are computed.
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Present:
Swansea: E.J. Beggs, D. Parashar and M. Schocker
Bangor: R. Brown, G. Evans, R. Lewis, T. Porter, C.D. Wensley
June 30, 2005
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