Quantum K\"ahlerian Lie groups from multiplicative unitaries
Abstract
We show that the deformation theory of Fr\'echet algebras for actions of K\"ahlerian Lie groups developed by two of us, leads in a natural way to examples of non-compact locally compact quantum groups. This is achieved by constructing a manageable multiplicative unitary out of the Fr\'echet deformation of for the action of and the undeformed coproduct. We also prove that these quantum groups are isomorphic to those constructed out of the unitary dual -cocycle discovered by Neshveyev and Tuset and associated with Bieliavsky's covariant -product, via the De Commer's results.
Keywords
Cite
@article{arxiv.1705.08326,
title = {Quantum K\"ahlerian Lie groups from multiplicative unitaries},
author = {P. Bieliavsky and Ph. Bonneau and F. D'Andrea and V. Gayral},
journal= {arXiv preprint arXiv:1705.08326},
year = {2019}
}
Comments
The present construction was based in an erroneous claim that the dual $2$-cocycle underlying the equivariant quantization of K\"ahlerian Lie groups is unitary. In fact, this cocycle is only a co-isometry. It turns that the deformed fundamental unitary that we have constructed is not unitary as well (but still satisfies the pentagonal equation)