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"From Quantum Groups to Unitary Modular Tensor Categories", Eric Rowell, 2006

Reviewed August 31, 2023

Citation: Rowell, Eric C. "From quantum groups to unitary modular tensor categories." Contemporary Mathematics 413 (2006): 215-230.

Web: https://arxiv.org/abs/math/0503226

Tags: Expository, Mathematical, Quantum-groups, Modular-tensor-categories, Pedagogical

As promised by the title, this paper gives a lovely survey of unitary modular tensor categories via the lens of quantum groups. In particular, the definition of UMTC is given (almost) in its entirety, with motivation given for (some of) the axioms. Hence, this paper serves as the best reference to give to a beginner for the definition of a UMTC.

The paper is fairly short, and the first few pages (which introduce UMTCs) require no knowledge of quantum groups. This is the paper I used to learn the definition of UMTC. Of course, this is no substitute for a proper textbook, like for instance

> Bakalov, Bojko, and Alexander A. Kirillov. Lectures on tensor categories and modular functors. Vol. 21. American Mathematical Soc., 2001.