New York Journal of Mathematics
Volume 5 (1999) 131-137


C. L. Schochet

The Topological Snake Lemma and Corona Algebras

Published: September 29, 1999
Keywords: Corona algebra, multiplier algebra, Snake Lemma, homological algebra for C*-algebras
Subject: Primary 18G35, 46L05; Secondary 22A05, 46L85

We establish versions of the Snake Lemma from homological algebra in the context of topological groups, Banach spaces, and operator algebras. We apply this tool to demonstrate that if f: B → B' is a quasi-unital C*-map of separable C*-algebras, so that it induces a map of Corona algebras \bar f: QB → QB' , and if f is mono, then the induced map \bar f is also mono.

Author information

Mathematics Department, Wayne State University, Detroit, MI 48202