The classification question for Leavitt path algebras

被引:48
作者
Abrams, G. [1 ]
Anh, P. N. [2 ]
Louly, A. [3 ]
Pardo, E. [3 ]
机构
[1] Univ Colorado, Dept Math, Colorado Springs, CO 80933 USA
[2] Hungarian Acad Sci, Renyi Inst Math, H-1364 Budapest, Hungary
[3] Univ Cadiz, Dept Matemat, Cadiz 11510, Spain
关键词
Leavitt path algebra; isomorphism; K-theory;
D O I
10.1016/j.jalgebra.2008.05.020
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
引用
收藏
页码:1983 / 2026
页数:44
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