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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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Isomorphisms between Leavitt algebras and their matrix rings

G. Abrams1 / P. N. Ánh2 / E. Pardo3

1 Department of Mathematics, University of Colorado, Colorado Springs, CO 80933, U.S.A. e-mail:

2 Rényi Institute of Mathematics, Hungarian Academy of Sciences, 1364 Budapest, Pf. 127, Hungary. e-mail:

3 Departamento de Matemáticas, Universidad de Cádiz, Apartado 40, 11510 Puerto Real (Cádiz), Spain. e-mail:

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2008, Issue 624, Pages 103–132, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2008.082, October 2008

Publication History:
Received:
2006-12-20
Revised:
2007-07-30
Published Online:
2008-10-29

Abstract

Let K be any field, let Ln denote the Leavitt algebra of type (1,n – 1) having coefficients in K, and let Md(Ln) denote the ring of d × d matrices over Ln. In our main result, we show that Md(Ln) ≅ Ln if and only if d and n – 1 are coprime. We use this isomorphism to answer a question posed in [W. Paschke and N. Salinas, Matrix algebras over , Michigan Math. J. 26 (1979), 3–12.] regarding isomorphisms between various C*-algebras. Furthermore, our result demonstrates that data about the K 0 structure is sufficient to distinguish up to isomorphism the algebras in an important class of purely infinite simple K-algebras.

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