Flow invariants in the classification of Leavitt path algebras

JOURNAL OF ALGEBRA

卷:333

Article

Abrams, Gene¹  Louly, Adel²  Pardo, Enrique²  Smith, Christopher¹ 

[1] Univ Colorado, Dept Math, Colorado Springs, CO 80918 USA

[2] Univ Cadiz, Dept Matemat, Fac Ciencias, Puerto Real 11510, Cadiz, Spain

关键词: Leavitt path algebra;    Morita equivalence;    Flow equivalence;    K-Theory;   

DOI  :  10.1016/j.jalgebra.2011.01.022

来源: Elsevier

【 摘 要 】

We analyze in the context of Leavitt path algebras some graph operations introduced in the context of symbolic dynamics by Williams. Parry and Sullivan, and Franks. We show that these operations induce Morita equivalence of the corresponding Leavitt path algebras. As a consequence we obtain our two main results: the first gives sufficient conditions for which the Leavitt path algebras in a certain class are Morita equivalent, while the second gives sufficient conditions which yield isomorphisms. We discuss a possible approach to establishing whether or not these conditions are also in fact necessary. In the final section we present many additional operations on graphs which preserve Morita equivalence (resp. isomorphism) of the corresponding Leavitt path algebras. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free