Flow invariants in the classification of Leavitt path algebras

Details Flow invariants in the classification of Leavitt path algebras Flow invariants in the classification of Leavitt path algebras

2008-12-02

arxiv.org/abs/0812.0553v4

Mathematics

Rings and Algebras

Final version. To appear in Journal of Algebra

Scientific paper

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.

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