arXiv subjects

Thomas Timmermann

Publications and source records attributed to Thomas Timmermann.

21 records · Page 2Linked to original sources

arXiv2007

Finite-dimensional Hopf C-bimodules and C-pseudo-multiplicative unitaries

Finite quantum groupoids can be described in many equivalent ways: In terms of the weak Hopf C*-algebras of Böhm, Nill, and Szlachányi or the finite-dimensional Hopf-von Neumann bimodules of Vallin, and in terms of finite-dimensional multiplicative partial isometries or the finite-dimensional pseudo-multiplicative unitaries of Vallin. In this short note, we show that in finite dimensions, the notions of a Hopf-von Neumann bimodule and of a pseudo-multiplicative unitary coincide with the notions of a concrete Hopf-C*-bimodule and of a C*-pseudo-multiplicative unitary, respectively.

math.OA↗

arXiv2007

$C^$-pseudo-Kac systems and duality for coactions of concrete Hopf $C^$-bimodules

We study coactions of concrete Hopf $C^{*}$-bimodules in the framework of (weak) $C^{*}$-pseudo-Kac systems, define reduced crossed products and dual coactions, and prove an analogue of Baaj-Skandalis duality.

math.OA↗

arXiv2007

C*-pseudo-multiplicative unitaries

We introduce $C^*$-pseudo-multiplicative unitaries and (concrete) Hopf $C^*$-bimodules, which are $C^*$-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 $C^*$-pseudo-multiplicative unitary two Hopf-$C^*$-bimodules and discuss examples related to locally compact groupoids.

math.OA↗

Thomas Timmermann

Finite-dimensional Hopf C*-bimodules and C*-pseudo-multiplicative unitaries

$C^*$-pseudo-Kac systems and duality for coactions of concrete Hopf $C^*$-bimodules

C*-pseudo-multiplicative unitaries

Finite-dimensional Hopf C-bimodules and C-pseudo-multiplicative unitaries

$C^$-pseudo-Kac systems and duality for coactions of concrete Hopf $C^$-bimodules