Examples of quantum commutants
Quantum Algebra
2011-04-12 v2 Operator Algebras
Abstract
We describe the notion of a quantum family of maps of a quantum space and that of a quantum commutant of such a family. Quantum commutants are quantum semigroups defined by a certain universal property. We give a few examples of these objects acting on a classical -point space and on the quantum space underlying the algebra of two by two matrices. We show that some of the resulting quantum semigroups are not compact quantum groups. The proof of one result touches on an interesting problem of the theory of compact quantum groups.
Cite
@article{arxiv.0806.0503,
title = {Examples of quantum commutants},
author = {Piotr M. Soltan},
journal= {arXiv preprint arXiv:0806.0503},
year = {2011}
}
Comments
11 pages, an error in one example corrected, typos corrected