English

The Lattice of C*-covers of an operator algebra

Operator Algebras 2025-01-16 v2

Abstract

In this paper it is shown that the lattice of C*-covers of an operator algebra does not contain enough information to distinguish operator algebras up to completely isometric isomorphism. In addition, four natural equivalences of the lattice of C*-covers are developed and proven to be distinct. The lattice of C*-covers of direct sums and tensor products are studied. Along the way key examples are found of an operator algebra that generates exactly n C*-algebras up to *-isomorphism and a simple operator algebra that is not similar to a C*-algebra.

Keywords

Cite

@article{arxiv.2304.02783,
  title  = {The Lattice of C*-covers of an operator algebra},
  author = {Adam Humeniuk and Christopher Ramsey},
  journal= {arXiv preprint arXiv:2304.02783},
  year   = {2025}
}

Comments

Accepted to the Canadian Journal of Mathematics