Unitarizablity of premodular categories

Details Unitarizablity of premodular categories Unitarizablity of premodular categories

2007-10-08

arxiv.org/abs/0710.1621v3

J. Pure Appl. Algebra, 212 no. 8 (2008) 1878-1887

Mathematics

Quantum Algebra

Version 2: proof of conjecture provided by referee, now Theorem 3.8 is sharp. To appear in J. Pure Appl. Algebra

Scientific paper

10.1016/j.jpaa.2007.11.004

We study the unitarizability of premodular categories constructed from representations of quantum group at roots of unity. We introduce \emph{Grothendieck unitarizability} as a natural generalization of unitarizability to any class of premodular categories with a common Grothendieck semiring. We obtain new results for quantum groups of Lie types $F_4$ and $G_2$, and improve the known results for Lie types $B$ and $C$.

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