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**Date:** 2009
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/1057820
**Description:** Higher-rank graphs (or k-graphs) were introduced by Kumjian and Pask to provide combinatorial models for the higher-rank Cuntz-Krieger C*-algebras of Robertson and Steger. Here we consider a family of... More
**Reviewed:**
**Date:** 2009
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/917012
**Description:** If a locally compact group G acts properly on a locally compact space X, then the induced action on C₀(X) is proper in the sense of Rieffel, with generalised fixed-point algebra C₀(GX). Rieffel's theo... More
**Reviewed:**
**Date:** 2007
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/803423
**Description:** The classical Chase–Harrison–Rosenberg exact sequence relates the Picard and Brauer groups of a Galois extension S of a commutative ring R to the group cohomology of the Galois group. We associate to ... More
**Reviewed:**
**Date:** 2007
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/926744
**Description:** We show that important structural properties of C*-algebras and the multiplicity numbers of representations are preserved under Morita equivalence.
**Reviewed:**
**Date:** 2006
**Keyword:** imprimitivity theorems | C*-algebras | induced algebras | Green's Imprimitivity Theorem | Mansfield's Imprimitivity Theorem
**Language:** eng
**Resource Type:** book
**Identifier:** http://hdl.handle.net/1959.13/923587
**Description:** Imprimitivity theorems provide a fundamental tool for studying the representation theory and structure of crossed-product C*-algebras. In this work, we show that the Imprimitivity Theorem for induced ... More
**Date:** 2006
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/926765
**Description:** We consider Exel’s new construction of a crossed product of a C*-algebra A by an endomorphism α. We prove that this crossed product is universal for an appropriate family of covariant representations,... More
**Reviewed:**
**Date:** 2006
**Resource Type:** journal article
**Identifier:** uon:6394
**Description:** We describe a class of rank-2 graphs whose C*-algebras are AT algebras. For a subclass which we call rank-2 Bratteli diagrams, we compute the K-theory of the C*-algebra.We identify rank-2 Bratteli dia... More
**Reviewed:**
**Date:** 2005
**Keyword:** c-asterisk-algebras | crossed-products | induced representations | star-algebras | morita equivalence | coactions
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/24433
**Description:** We prove a symmetric imprimitivity theorem for commuting proper actions of locally compact groups H and K on a C*-algebra.
**Reviewed:**
**Date:** 2005
**Keyword:** k-graph | small category | covering | fundamental group | c*-algebra | coaction | c-asterisk-algebras | higher-rank graphs | crossed-products | directed-graphs | coactions | bundles
**Language:** eng
**Resource Type:** journal article
**Identifier:** uon:420
**Description:** k-graphs are higher-rank analogues of directed graphs which were first developed to provide combinatorial models for operator algebras of Cuntz-Krieger type. Here we develop the theory of covering spa... More
**Reviewed:**
**Creators:**
Raeburn, Iain
**Date:** 2005
**Language:** eng
**Resource Type:** book
**Identifier:** http://hdl.handle.net/1959.13/35056
**Description:** Graph algebras are a family of operator algebras which are associated to directed graphs. These algebras have an attractive structure theory in which algebraic properties of the algebra are related to... More
**Creators:**
Baumgartner, Udo | Foster, James | Hicks, Jacqueline | Lindsay, Helen | Maloney, Ben | Raeburn, Iain | Ramagge, Jacqui | Richardson, Sarah
**Date:** 2005
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/29129
**Description:** We describe the Hecke algebra ℋ(Γ,Γ₀) of a Hecke pair (Γ,Γ₀) in terms of the Hecke pair (N,Γ₀) where N is a normal subgroup of Γ containing Γ₀. To do this, we introduce twisted crossed products of uni... More
**Reviewed:**
**Creators:**
Baumgartner, Udo | Foster, James | Hicks, Jacqueline | Lindsay, Helen | Maloney, Ben | Raeburn, Iain | Ramagge, Jacqueline | Richardson, Sarah
**Date:** 2005
**Keyword:** Hecke algebras | representation | twisted crossed product by semigroups | semigroup crossed product
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/24470
**Description:** We describe the Hecke algebra H(Gamma,Gamma(0)) of a Hecke pair (Gamma, Gamma(0)) in terms of the Hecke pair (N, Gamma(0)) where N is a normal subgroup of Gamma containing Gamma(0). To do this, we int... More
**Reviewed:**
**Date:** 2005
**Keyword:** C*-algebra of directed graphs | Hilbert bimodules | Toeplitz algebras | product systems of graphs | c-asterisk-algebras | cuntz-krieger algebras | hilbert bimodules | infinite-graphs | cstar-algebras
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/25304
**Description:** There has recently been much interest in the C*-algebras of directed graphs. Here we consider product systems E of directed graphs over sernigroups and associated C*-algebras C* (E) and TC* (E) which ... More
**Reviewed:**
**Date:** 2005
**Language:** eng
**Resource Type:** journal article
**Identifier:** uon:80
**Description:** We realize the Hecke C*-algebra C-Q of Bost and Connes as a direct limit of Hecke C*-algebras which are semigroup crossed products by N-F, for F a finite set of primes. For each approximating Hecke C*... More
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**Reviewed:**
**Date:** 2004
**Resource Type:** journal article
**Identifier:** uon:6386
**Description:** We generalise the theory of Cuntz–Krieger families andgraph algebras to the class of finitely aligned k-graphs. This class contains in particular all row-finite k-graphs. The Cuntz–Krieger relations f... More
**Reviewed:**