English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

This paper deals with some related problems posed by Doplicher-Roberts,Seiberg-Moore, Frenkel-Zhu, Huang regarding relations between quantum groups atroots of unity and categories arising from conformal field theory. We constructunitary rigid ribbon braided tensor category structures on module categories ofaffine vertex operator algebras at positive integer levels for all Lie types,derived from fusion categories of quantum groups via the construction ofcertain semisimple weak Hopf algebras having roots in the work by Mack andSchomerus, and a Drinfeld twist to the Zhu algebra analogous to Drinfeld twistfor the quantized universal enveloping algebra U_h(g) and Drinfeld quasi-Hopfalgebra structure over U(g). We use our construction to give a direct proof ofan equivalence theorem (going back to Kazhdan-Lusztig and Finkelberg for affineLie algebras) between fusion categories of quantum groups and affine vertexoperator algebras at positive integer levels, with respect to Huang-Lepowskyribbon braided tensor structure, for the classical Lie types and G_2. We applythis result to unitarize ribbon braided module categories of vertex operatoralgebras. We classify fusion categories with type A fusion rules by theirribbon structure. In our work, the unitary structure of quantum group fusioncategories obtained by Wenzl and an associated fibre functor to the Hilbertspaces play a main role to construct naturally associated semisimple weak Hopfalgebras.

Weak quasi-Hopf algebras, C*-tensor categories and conformal field theory, and the Kazhdan-Lusztig-Finkelberg theorem