Crossed Products by Semigroups of Endomorphisms and the Toeplitz Algebras of Ordered Groups

DOI10.2307/2161182zbMath0818.46071OpenAlexW4239035091MaRDI QIDQ4318345

Iain Raeburn, May Nilsen, Marcelo Laca, Sriwulan Adji

Publication date: 16 February 1995

Full work available at URL: https://doi.org/10.2307/2161182

zbMATH Keywords

crossed productsendomorphismToeplitz algebracovariant representationsemigroup of isometries\(C^*\)- algebrasnonunitary isometriespositive cone in a totally ordered Abelian grouprepresentation of the crossed product is faithful

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Ordered groups (06F15)

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Cites Work

• Unnamed Item
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• Ordered groups and crossed products of \(C^*\)-algebras
• Simple \(C^*\)-algebras generated by isometries
• On the \(C^*\)-algebra of a one-parameter semigroup of isometries
• On crossed products and Takai duality
• The Crossed Product of a C ∗ -Algebra by an Endomorphism
• Faithful Representations of Crossed Products by Endomorphisms
• The 𝐶*-algebra generated by an isometry
• Inductive Limits of Finite Dimensional C ∗ -Algebras