C*-pseudo-multiplicative unitaries

Abstract

We introduce $C^{\ast }$-pseudo-multiplicative unitaries and (concrete) Hopf $C^{\ast }$-bimodules, which are $C^{\ast }$-algebraic variants of the pseudo-multiplicative unitaries on Hilbert spaces and the Hopf-von Neumann-bimodules studied by Enock, Lesieur, Vallin. Moreover, we associate to every regular $C^{\ast }$-pseudo-multiplicative unitary two Hopf-$C^{\ast }$-bimodules and discuss examples related to locally compact groupoids.

29 pages

Cited by in corpus (6)

• The relative tensor product and a minimal fiber product in the setting of $C^{\ast }$-algebras
• Measured quantum groupoids with a central basis
• $C^{\ast }$-pseudo-Kac systems and duality for coactions of concrete Hopf $C^{\ast }$-bimodules
• From Hopf C*-families to concrete Hopf C*-bimodules
• Finite-dimensional Hopf C*-bimodules and C*-pseudo-multiplicative unitaries
• Compact C*-quantum groupoids