A Note on the Quantum Family of Maps
Quantum Algebra
2018-10-23 v2
Abstract
The notion and theory of the quantum space of all maps from a quantum space pioneered by So{\l}tan have been mainly focused on finite-dimensional C*-algebras which are matrix algebra bundles over a finite set . We propose a modification of this notion to cover the case of for general compact Hausdorff spaces instead of finite sets while taking into account of the topology of . A notion of free product of copies of a unital C*-algebra topologically indexed by a compact Hausdorff space arises naturally, and satisfies some desired functoriality.
Cite
@article{arxiv.1809.11107,
title = {A Note on the Quantum Family of Maps},
author = {Albert Jeu-Liang Sheu and Thomas Timmermann},
journal= {arXiv preprint arXiv:1809.11107},
year = {2018}
}