Isomorphism and Morita equivalence of graph algebras
By G. Abrams, M. Tomforde. 2008
77 citations recorded by the source corpus.
For any countable graph E, we investigate the relationship between the Leavitt path algebra L ℂ (E) and the graph C * -algebra C * (E). For graphs E and F, we examine ring homomorphisms, ring *-homomorphisms, algebra homomorphisms, and algebra *-homomorphisms between L ℂ (E) and L ℂ (F). We prove that in certain situations isomorphisms between L ℂ (E) and L ℂ (F) yield *-isomorphisms between the corresponding C * -algebras C * (E) and C * (F). Conversely, we show that *-isomorphisms between C * (E) and C * (F) produce isomorphisms between L ℂ (E) and L ℂ (F) in specific cases. The relationship between Leavitt path algebras and graph C * -algebras is also explored in the context of Morita equivalence.
Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/0f7c65b81cd75096235aa06dccdf900a1ff5562f
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In Algebra and Number Theory
- S. P. Smith
- G. Abrams
- Roozbeh Hazrat
- M. Tomforde
- G. Pino
- Mercedes Siles Molina
- Kulumani M. Rangaswamy
- Xiao-Wu Chen
In Mathematical Physics
- S. P. Smith
- G. Abrams
- Roozbeh Hazrat
- M. Tomforde
- G. Pino
- Mercedes Siles Molina
- Kulumani M. Rangaswamy
- Xiao-Wu Chen
In Statistical and Nonlinear Physics
- S. P. Smith
- G. Abrams
- M. Tomforde
- G. Pino
- Roozbeh Hazrat
- Mercedes Siles Molina
- Kulumani M. Rangaswamy
Citations in the corpus
- Leavitt path algebras: the first decade (2014, methodology): “The initial study of C-algebras corresponding to arbitrary graphs appears in [18] (2013), where this notion was utilized to give the first systematic construction of C-algebras which are prime but not primitive.”
- CATEGORY EQUIVALENCES INVOLVING GRADED MODULES OVER PATH ALGEBRAS OF QUIVERS (2011, background): “However, it is not the convention adopted in [1] (see [1, Defn.”