Journal of Noncommutative Geometry


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Volume 14, Issue 1, 2020, pp. 105–123
DOI: 10.4171/JNCG/360

Published online: 2020-04-30

Quantum groups with projection and extensions of locally compact quantum groups

Paweł Kasprzak[1] and Piotr M. Sołtan[2]

(1) University of Warsaw, Poland
(2) University of Warsaw, Poland

The main result of the paper is the characterization of those locally compact quantum groups with projection, i.e. non-commutative analogs of semidirect products, which are extensions as defined by L. Vainerman and S. Vaes. It turns out that quantum groups with projection are usually not extensions.We discuss several examples including the quantum $\mathrm{U}_q(2)$. The major tool used to obtain these results is the co-duality for coideals in algebras of functions on locally compact quantum groups and the concept of a normal coideal.

Keywords: Quantum group with projection, extension of locally compact quantum groups, von Neumann algebra

Kasprzak Paweł, Sołtan Piotr: Quantum groups with projection and extensions of locally compact quantum groups. J. Noncommut. Geom. 14 (2020), 105-123. doi: 10.4171/JNCG/360