期刊
JOURNAL OF ALGEBRA
卷 320, 期 5, 页码 1983-2026出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jalgebra.2008.05.020
关键词
Leavitt path algebra; isomorphism; K-theory
类别
资金
- Hungarian National Foundation for Scientific Research [K61007]
- The Colorado College, the University of Colorado at Colorado Springs
- Post-doctoral fellow of the A.E.C.I. (Spain)
- DGI and European Regional Development Fund [MTM2004-00149, MTM2007-60338]
- PAI [FQM-298, P06-FQM-1889]
- Comissionat per Universitats i Recerca de la Generalitat de Catalunya
We prove an algebraic version of the Gauge-Invariant Uniqueness Theorem, a result which gives information about the injectivity of certain homomorphisms between Z-graded algebras. As our main application of this theorem, we obtain isomorphisms between the Leavitt path algebras of specified graphs. From these isomorphisms we are able to achieve two ends. First, we show that the K-0 groups of various sets of purely infinite simple Leavitt path algebras, together with the position of the identity element in K0, classify the algebras in these sets up to isomorphism. Second, we show that the isomorphism between matrix rings over the classical Leavitt algebras, established previously using number-theoretic methods, can be reobtained via appropriate isomorphisms between Leavitt path algebras. (C) 2008 Elsevier Inc. All rights reserved.
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