Quantum families of maps and quantum semigroups on finite quantum spaces
Operator Algebras
2015-06-26 v5 Quantum Algebra
Abstract
Quantum families of maps between quantum spaces are defined and studied. We prove that quantum semigroup (and sometimes quantum group) structures arise naturally on such objects out of more fundamental properties. As particular cases we study quantum semigroups of maps preserving a fixed state and quantum commutants of given quantum families of maps.
Keywords
Cite
@article{arxiv.math/0610922,
title = {Quantum families of maps and quantum semigroups on finite quantum spaces},
author = {Piotr M. Soltan},
journal= {arXiv preprint arXiv:math/0610922},
year = {2015}
}
Comments
update: last section generalized to non-tracial states