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Group gradations on Leavitt path algebras
Högskolan Väst, SWE.
Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.ORCID iD: 0000-0001-8095-0820
2019 (English)In: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829Article in journal (Refereed) Epub ahead of print
Abstract [en]

Given a directed graph E and an associative unital ring R one may define the Leavitt path algebra with coefficients in R, denoted by LR(E). For an arbitrary group G, LR(E) can be viewed as a G-graded ring. In this paper, we show that LR(E) is always nearly epsilon-strongly G-graded. We also show that if E is finite, then LR(E) is epsilon-strongly G-graded. We present a new proof of Hazrat's characterization of strongly g-graded Leavitt path algebras, when E is finite. Moreover, if E is row-finite and has no source, then we show that LR(E) is strongly-graded if and only if E has no sink. We also use a result concerning Frobenius epsilon-strongly G-graded rings, where G is finite, to obtain criteria which ensure that LR(E) is Frobenius over its identity component. © 2020 World Scientific Publishing Company.

Place, publisher, year, edition, pages
World Scientific Publishing Co. Pte Ltd , 2019.
Keywords [en]
epsilon-strongly graded ring, Leavitt path algebra, S-Unital ring, strongly graded ring
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:bth-18645DOI: 10.1142/S0219498820501650Scopus ID: 2-s2.0-85071375607OAI: oai:DiVA.org:bth-18645DiVA, id: diva2:1350551
Available from: 2019-09-11 Created: 2019-09-11 Last updated: 2019-09-11Bibliographically approved

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Öinert, Johan

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