SAW*-algebras are essentially non-factorizable

TL;DR

This paper proves that SAW*-algebras cannot be decomposed into tensor products of two infinite-dimensional C*-algebras, answering a question about the structure of the Calkin algebra and related algebras.

Contribution

It establishes a fundamental non-factorizability property of SAW*-algebras, extending the understanding of their algebraic structure and answering a specific open question.

Findings

No surjective *-homomorphism from SAW*-algebras onto tensor products of two infinite-dimensional C*-algebras.

The Calkin algebra cannot be expressed as a tensor product of two infinite-dimensional C*-algebras.

SAW*-algebras exhibit a form of algebraic rigidity preventing such factorizations.

Abstract

In this paper we solve a question of Simon Wassermann, whether the Calkin algebra can be written as a C*-tensor product of two infinite dimensional C*-algebras. More generally we show that there is no surjective *-homomorphism from a SAW*-algebra onto C*-tensor product of two infinite dimensional C*-algebras.