The classification question for Leavitt path algebras

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URI: http://hdl.handle.net/10498/16095
DOI: 10.1016/j.jalgebra.2008.05.020
ISSN: 0021-8693
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2008-01-01Department
MatemáticasSource
Journal of Algebra 320 (2008), 1983-2026Abstract
We prove an algebraic version of the Gauge-Invariant Uniqueness Theorem, a result which gives information about the injectivity of certain homomorphisms between ZZ-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 K0K0 groups of various sets of purely infinite simple Leavitt path algebras, together with the position of the identity element in K0K0, 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
Subjects
Leavitt path algebra; Isomorphism; K-theoryCollections
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- Articulos Científicos Matemáticas [162]