Recent developments of the categorical Verlinde formula
Kenichi Shimizu (Shibaura Institute of Technology)
TL;DR
This paper reviews recent progress in understanding the categorical Verlinde formula within non-semisimple modular tensor categories, highlighting theoretical advancements in algebraic and topological quantum field theories.
Contribution
It provides a comprehensive overview of the developments in non-semisimple modular tensor categories and their associated Verlinde formula, expanding the mathematical framework beyond semisimple cases.
Findings
Advances in non-semisimple modular tensor categories
Extensions of the categorical Verlinde formula
Implications for quantum topology and algebra
Abstract
I review recent developments of "non-semisimple" modular tensor categories in the sense of Lyubashenko and the categorical Verlinde formula for such categories (this is a proceedings article for Meeting for Study of Number theory, Hopf algebras and related topics held at University of Toyama, Japan, 12-15 February 2017).
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry