Quantum groups with projection on von Neumann algebra level
Operator Algebras
2014-10-17 v2 Quantum Algebra
Abstract
We introduce an axiomatization of the notion of a semidirect product of locally compact quantum groups and study properties. Our approach is slightly different from the one introduced in the thesis of S.~Roy and, unlike the investigations of Roy, we work within the von Neumann algebraic picture. This allows the use of powerful techniques related to crossed products by actions of locally compact quantum groups. In particular we show existence of a "braided comultiplication" on the algebra spanned by slices of "braided multiplicative unitary".
Cite
@article{arxiv.1410.1405,
title = {Quantum groups with projection on von Neumann algebra level},
author = {Paweł Kasprzak and Piotr M. Sołtan},
journal= {arXiv preprint arXiv:1410.1405},
year = {2014}
}
Comments
Several typos corrected, list of references updated, a proposition establishing an analogue of Podle\'s condition added, presentation (hopefully) improved