Weak C^*-Hopf Algebras and Multiplicative Isometries

Details Weak C^*-Hopf Algebras and Multiplicative Isometries Weak C^*-Hopf Algebras and Multiplicative Isometries

1998-10-12

arxiv.org/abs/math/9810070v1

Mathematics

Quantum Algebra

23 pages, LaTeX

Scientific paper

We show how the data of a finite dimensional weak C^*-Hopf algebra can be encoded into a pair (H,V) where H is a finite dimensional Hilbert space and V: H \o H --> H \o H is a partial isometry satisfying, among others, the pentagon equation. In case of V being unitary we recover the Baaj-Skandalis multiplicative unitary of the discrete compact type. Relation to the pseudo- multiplicative unitary approach proposed by J.-M. Vallin and M. Enock is also discussed.

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