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