Fusion rings and fusion ideals: PhD dissertation

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  • Troels Bak Andersen, Denmark
This dissertation investigates fusion rings, which are Grothendieck groups of rigid, monoidal, semisimple, abelian categories. Special interest is in rational fusion rings, i.e., fusion rings which admit a finite basis, for as commutative rings they may be presented as quotients of polynomial rings by the so-called fusion ideals.

The fusion rings of Wess-Zumino-Witten models have been widely studied and are well understood in terms of precise combinatorial descriptions and explicit generating sets of the fusion ideals. They also appear in another, more general, setting via tilting modules for quantum groups at complex roots of unity. The main goal of this dissertation is to generalize previous results to this setting.
Original languageEnglish
PublisherCentre for Quantum Geometry of Moduli Spaces, Aarhus University
Number of pages95
Publication statusPublished - 28 Jul 2014

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