Hereditarily antisymmetric operator algebras

Abstract

We introduce a notion of ``hereditarily antisymmetric'' operator algebras and prove a structure theorem for them in finite dimensions. We also characterize those operator algebras in finite dimensions which can be made upper triangular and prove matrix analogs of the theorems of Dilworth and Mirsky for finite posets. Some partial results are obtained in the infinite dimensional case.

34 pages; added a section to explain the physical interpretation

References in corpus (2)

• Zero-error communication via quantum channels, non-commutative graphs and a quantum Lovasz theta function
• A von Neumann algebra approach to quantum metrics

Cited by in corpus (3)

• Quantum CPOs
• A category of quantum posets
• Discrete quantum structures