Weak C-Hopf Algebras and Multiplicative Isometries

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⊗H → H⊗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 pseudomultiplicative unitary approach proposed by J.-M. Vallin and M. Enock is also discussed. E-mail: [email protected] Supported by the Hungarian Scientific Research Fund, OTKA – T 016 233 E-mail: [email protected] Supported by the Hungarian Scientific Research Fund, OTKA – T 020 285.