Weak C*-Hopf algebras and multiplicative isometries

G. Böhm, Kornél Szlachányi

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 languageEnglish
Pages (from-to)357-376
Number of pages20
JournalJournal of Operator Theory
Volume45
Issue number2
Publication statusPublished - 2001

Fingerprint

Hopf Algebra
Isometry
Multiplicative
Partial Isometry
Pentagon
Hilbert space

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

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

In: Journal of Operator Theory, Vol. 45, No. 2, 2001, p. 357-376.

Research output: Contribution to journalArticle

Böhm, G & Szlachányi, K 2001, 'Weak C*-Hopf algebras and multiplicative isometries', Journal of Operator Theory, vol. 45, no. 2, pp. 357-376.
Böhm, G. ; Szlachányi, Kornél. / Weak C*-Hopf algebras and multiplicative isometries. In: Journal of Operator Theory. 2001 ; Vol. 45, No. 2. pp. 357-376.
@article{d7369f18504641408725ef7a07efc324,
title = "Weak C*-Hopf algebras and multiplicative isometries",
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.",
keywords = "Multiplicative partial isometries, Pseudo-multiplicative unitaries, Weak Hopf algebras",
author = "G. B{\"o}hm and Korn{\'e}l Szlach{\'a}nyi",
year = "2001",
language = "English",
volume = "45",
pages = "357--376",
journal = "Journal of Operator Theory",
issn = "0379-4024",
publisher = "Theta Foundation",
number = "2",

}

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 -