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Isomorphisms between Leavitt algebras and their matrix rings
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G. Abrams
Published/Copyright:
October 29, 2008
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 K0 structure is sufficient to distinguish up to isomorphism the algebras in an important class of purely infinite simple K-algebras.
Received: 2006-12-20
Revised: 2007-07-30
Published Online: 2008-10-29
Published in Print: 2008-November
© Walter de Gruyter Berlin · New York 2008
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- The spinorial τ-invariant and 0-dimensional surgery
- Well-posedness, blow-up phenomena, and global solutions for the b-equation
- Siegel disks and periodic rays of entire functions
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Articles in the same Issue
- Topology of negatively curved real affine algebraic surfaces
- The spinorial τ-invariant and 0-dimensional surgery
- Well-posedness, blow-up phenomena, and global solutions for the b-equation
- Siegel disks and periodic rays of entire functions
- Isomorphisms between Leavitt algebras and their matrix rings
- The number of smallest parts in the partitions of n
- Modular analogues of Jordan's theorem for finite linear groups
- Prime specialization in higher genus I
- Filling inequalities do not depend on topology
- Erratum to "Modular curves and Ramanujan's continued fraction"
