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- W2950883984 abstract "We show that the left regular representation pi_l of a discrete quantum group (A,Delta) has the absorbing property and forms a monoid (pi_l,tilde{m},tilde{eta}) in the representation category Rep(A,Delta). Next we show that an absorbing monoid in an abstract tensor *-category C gives rise to an embedding functor E:C->Vect_C, and we identify conditions on the monoid, satisfied by (pi_l,tilde{m},tilde{eta}), implying that E is *-preserving. As is well-known, from an embedding functor E: C->mathrm{Hilb} the generalized Tannaka theorem produces a discrete quantum group (A,Delta) such that C is equivalent to Rep_f(A,Delta). Thus, for a C^*-tensor category C with conjugates and irreducible unit the following are equivalent: (1) C is equivalent to the representation category of a discrete quantum group (A,Delta), (2) C admits an absorbing monoid, (3) there exists a *-preserving embedding functor E: C->mathrm{Hilb}." @default.
- W2950883984 created "2019-06-27" @default.
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- W2950883984 date "2006-04-04" @default.
- W2950883984 modified "2023-09-27" @default.
- W2950883984 title "Monoids, Embedding Functors and Quantum Groups" @default.
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