Unital algebras being Morita equivalent to weighted Leavitt path algebras

2023/12/25 by Roozbeh Hazrat, Hazrat, Roozbeh, Tran Giang Nam +1
Mathematics · Medicine · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Intracranial Aneurysms: Treatment and Complications #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2312.15704

openalex publication_date 2023/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we describe the endomorphism ring of a finitely generated progenerator module of a weighted Leavitt path algebra L_K(E, w) of a finite vertex weighted graph (E, w). Contrary to the case of Leavitt path algebras, we show that a (full) corner of a weighted Leavitt path algebra is, in general, not isomorphic to a weighted Leavitt path algebra. However, using the above result, we show that for every full idempotent ε in L_K(E, w), there exists a positive integer n such that M_n(εL_K(E, w) ε) is isomorphic to the weighted Leavitt path algebra of a weighted graph explicitly constructed from (E, w). We then completely describe unital algebras being Morita equivalent to weighted Leavitt path algebras of vertex weighted graphs. In particular, we characterize unital algebras being Morita equivalent to sandpile algebras.

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