## Isomorphism and Morita equivalence of graph algebras

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- by Gene Abrams and Mark Tomforde PDF
- Trans. Amer. Math. Soc.
**363**(2011), 3733-3767 Request permission

## Abstract:

For any countable graph $E$, we investigate the relationship between the Leavitt path algebra $L_{\mathbb {C}}(E)$ and the graph $C^*$-algebra $C^*(E)$. For graphs $E$ and $F$, we examine ring homomorphisms, ring $*$-homomorphisms, algebra homomorphisms, and algebra $*$-homomorphisms between $L_{\mathbb {C}}(E)$ and $L_{\mathbb {C}}(F)$. We prove that in certain situations isomorphisms between $L_{\mathbb {C}}(E)$ and $L_{\mathbb {C}}(F)$ 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 $L_{\mathbb {C}}(E)$ and $L_{\mathbb {C}}(F)$ in specific cases. The relationship between Leavitt path algebras and graph $C^*$-algebras is also explored in the context of Morita equivalence.## References

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## Additional Information

**Gene Abrams**- Affiliation: Department of Mathematics, University of Colorado, Colorado Springs, Colorado 80933
- MR Author ID: 190273
- Email: abrams@math.uccs.edu
**Mark Tomforde**- Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204-3008
- MR Author ID: 687274
- Email: tomforde@math.uh.edu
- Received by editor(s): October 15, 2008
- Received by editor(s) in revised form: December 8, 2009
- Published electronically: February 4, 2011
- © Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**363**(2011), 3733-3767 - MSC (2010): Primary 16D70, 46L55
- DOI: https://doi.org/10.1090/S0002-9947-2011-05264-5
- MathSciNet review: 2775826