Corners of Leavitt path algebras of finite graphs are Leavitt path algebras

JOURNAL OF ALGEBRA

卷:547

Article

Abrams, Gene¹  Tran Giang Nam² 

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

[2] VAST, Inst Math, 18 Hoang Quoc Viet, Hanoi, Vietnam

关键词: Leavitt path algebra;    Morita equivalence;   

DOI  :  10.1016/j.jalgebra.2019.11.020

来源: Elsevier

【 摘 要 】

We achieve an extremely useful description (up to isomorphism) of the Leavitt path algebra L-K(E) of a finite graph E with coefficients in a field K as a direct sum of matrix rings over K, direct sum with a corner of the Leavitt path algebra L-K(F) of a graph F for which every regular vertex is the base of a loop. Moreover, in this case one may transform the graph E into the graph F via some step-by-step procedure, using the source elimination and collapsing processes. We use this to establish the main result of the article, that every nonzero corner of a Leavitt path algebra of a finite graph is isomorphic to a Leavitt path algebra. Indeed, we prove a more general result, to wit, that the endomorphism ring of any nonzero finitely generated projective L-K(E)-module is isomorphic to the Leavitt path algebra of a graph explicitly constructed from E. Consequently, this yields in particular that every unital K-algebra which is Morita equivalent to a Leavitt path algebra is indeed isomorphic to a Leavitt path algebra. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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