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

Sriwulan Adji; Marcelo Laca; May Nilsen; Iain Raeburn

doi:10.1090/S0002-9939-1994-1215024-1

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

Sriwulan Adji, Marcelo Laca, May Nilsen, Iain Raeburn

Research output: Contribution to journal › Article › peer-review

66 Scopus citations

Abstract

Let ℸ⁺ be the positive cone in a totally ordered abelian group ℸ. We construct crossed products by actions of ℸ⁺ as endomorphisms of Calgebras, and give criteria which ensure a given representation of the crossed product is faithful. We use this to prove that the C* -algebras generated by two semigroups V, W: ℸ⁺ → B (H) 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.

Original language	English (US)
Pages (from-to)	1133-1141
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	122
Issue number	4
DOIs	https://doi.org/10.1090/S0002-9939-1994-1215024-1
State	Published - Dec 1994
Externally published	Yes

Keywords

C*-algebra
Covariant representation
Crossed product
Endomorphism
Ordered group
Semigroup of isometries
Toeplitz algebra

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-1994-1215024-1

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abstract = "Let ℸ+ be the positive cone in a totally ordered abelian group ℸ. We construct crossed products by actions of ℸ+ as endomorphisms of Calgebras, and give criteria which ensure a given representation of the crossed product is faithful. We use this to prove that the C* -algebras generated by two semigroups V, W: ℸ+ → B (H) 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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T1 - Crossed products by semigroups of endomorphisms and the toeplitz algebras of ordered groups

AU - Adji, Sriwulan

AU - Laca, Marcelo

AU - Nilsen, May

AU - Raeburn, Iain

PY - 1994/12

Y1 - 1994/12

N2 - Let ℸ+ be the positive cone in a totally ordered abelian group ℸ. We construct crossed products by actions of ℸ+ as endomorphisms of Calgebras, and give criteria which ensure a given representation of the crossed product is faithful. We use this to prove that the C* -algebras generated by two semigroups V, W: ℸ+ → B (H) 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.

AB - Let ℸ+ be the positive cone in a totally ordered abelian group ℸ. We construct crossed products by actions of ℸ+ as endomorphisms of Calgebras, and give criteria which ensure a given representation of the crossed product is faithful. We use this to prove that the C* -algebras generated by two semigroups V, W: ℸ+ → B (H) 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.

KW - C-algebra

KW - Covariant representation

KW - Crossed product

KW - Endomorphism

KW - Ordered group

KW - Semigroup of isometries

KW - Toeplitz algebra

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JO - Proceedings of the American Mathematical Society

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

Abstract

Keywords

ASJC Scopus subject areas

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