Crossed products by semigroups of endomorphisms and the Toeplitz algebras of ordered groups

Authors:
Sriwulan Adji, Marcelo Laca, May Nilsen and Iain Raeburn

Journal:
Proc. Amer. Math. Soc. **122** (1994), 1133-1141

MSC:
Primary 46L55; Secondary 46L05, 47B35, 47D03

DOI:
https://doi.org/10.1090/S0002-9939-1994-1215024-1

MathSciNet review:
1215024

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the positive cone in a totally ordered abelian group . We construct crossed products by actions of as endomorphisms of -algebras, and give criteria which ensure a given representation of the crossed product is faithful. We use this to prove that the -algebras generated by two semigroups *V*, of nonunitary isometries are canonically isomorphic, thus giving a new, self-contained proof of a theorem of Murphy, which includes earlier results of Coburn and Douglas.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1215024-1

Keywords:
-algebra,
endomorphism,
ordered group,
covariant representation,
crossed product,
semigroup of isometries,
Toeplitz algebra

Article copyright:
© Copyright 1994
American Mathematical Society