From Quantum Groups to Unitary Modular Tensor Categories

Details From Quantum Groups to Unitary Modular Tensor Categories From Quantum Groups to Unitary Modular Tensor Categories

2005-03-11

arxiv.org/abs/math/0503226v3

Mathematics

Quantum Algebra

16 pages, final version to appear in Contemporary Mathematics. Version 2: minor typos fixed, references updated, Theorem 4.5 c

Scientific paper

Modular tensor categories are generalizations of the representation categories of quantum groups at roots of unity axiomatizing the properties necessary to produce 3-dimensional TQFTs. Although other constructions have since been found, quantum groups remain the most prolific source. Recently proposed applications to quantum computing have provided an impetus to understand and describe these examples as explicitly as possible, especially those that are "physically feasible." We survey the current status of the problem of producing unitary modular tensor categories from quantum groups, emphasizing explicit computations.

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