English

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 SS. We propose a modification of this notion to cover the case of C(X)C\left( X\right) for general compact Hausdorff spaces XX instead of finite sets SS while taking into account of the topology of XX. 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.

Keywords

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}
}