- Title
- Proper Actions on Graph Algebras
- Creator
- Marelli, Damián
- Resource Type
- thesis
- Date
- 2003
- Description
- Bachelor Honours - Bachelor of Mathematics (Honours)
- Description
- The c*-algebra C*(E) of a discrete graph E is generated by a family of orthogonal projections and partial isometries. If a discrete group G acts on E, this action induces an action of G on C*(E). In [5], Kumijan and Pask showed that if E is locally finite and the action G on C*E is free, then the C*-algebra C*(GE) of the quotient graph is Morita equivalent to the crossed product C*(E) Xα G. This result has a striking similarity with a theorem of Green [3, Theorem 14], which implies that, if X is a locally compact space and G is a locally compact group which acts freely and properly on X, then C₀(GX) (the C*-algebra of continuous functions ∫:GX → ℂ such that for all ∈>0, the set {z ∈ GX : |∫(z)|≥∈} is compact) is Morita equivalent to the crossed product C₀(X) Xα G.
- Subject
- orthogonal projections; partial isometries; graph algebras; theorem of Green; honours
- Identifier
- http://hdl.handle.net/1959.13/1056355
- Identifier
- uon:16032
- Rights
- Copyright 2003 Damián Marelli
- Language
- eng
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