Hopf algebras and finite tensor categories in conformal field theory - High Energy Physics - TheoryReport as inadecuate




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Abstract: In conformal field theory the understanding of correlation functions can bedivided into two distinct conceptual levels: The analytic properties of thecorrelators endow the representation categories of the underlying chiralsymmetry algebras with additional structure, which in suitable cases is the oneof a finite tensor category. The problem of specifying the correlators can thenbe encoded in algebraic structure internal to those categories. After reviewingresults for conformal field theories for which these representation categoriesare semisimple, we explain what is known about representation categories ofchiral symmetry algebras that are not semisimple. We focus on generalizationsof the Verlinde formula, for which certain finite-dimensional complex Hopfalgebras are used as a tool, and on the structural importance of the presenceof a Hopf algebra internal to finite tensor categories.



Author: Jurgen Fuchs, Christoph Schweigert

Source: https://arxiv.org/



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