### Abstract

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 with the pseudomultiplicative unitary approach proposed by J.-M. Vallin and M. Enock is also discussed.

Original language | English |
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Pages (from-to) | 357-376 |

Number of pages | 20 |

Journal | Journal of Operator Theory |

Volume | 45 |

Issue number | 2 |

Publication status | Published - 2001 |

### Fingerprint

### Keywords

- Multiplicative partial isometries
- Pseudo-multiplicative unitaries
- Weak Hopf algebras

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Operator Theory*,

*45*(2), 357-376.

**Weak C*-Hopf algebras and multiplicative isometries.** / Böhm, G.; Szlachányi, Kornél.

Research output: Contribution to journal › Article

*Journal of Operator Theory*, vol. 45, no. 2, pp. 357-376.

}

TY - JOUR

T1 - Weak C*-Hopf algebras and multiplicative isometries

AU - Böhm, G.

AU - Szlachányi, Kornél

PY - 2001

Y1 - 2001

N2 - 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 with the pseudomultiplicative unitary approach proposed by J.-M. Vallin and M. Enock is also discussed.

AB - 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 with the pseudomultiplicative unitary approach proposed by J.-M. Vallin and M. Enock is also discussed.

KW - Multiplicative partial isometries

KW - Pseudo-multiplicative unitaries

KW - Weak Hopf algebras

UR - http://www.scopus.com/inward/record.url?scp=17544393647&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17544393647&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:17544393647

VL - 45

SP - 357

EP - 376

JO - Journal of Operator Theory

JF - Journal of Operator Theory

SN - 0379-4024

IS - 2

ER -