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Group gradations on Leavitt path algebras
University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.ORCID iD: 0000-0001-6594-7041
Blekinge Institute of Technology, Department of Mathematics and Natural Sciences, Karlskrona, SE-37179, Sweden.
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
2019.
Keywords [en]
s -unital ring, strongly graded ring, epsilon-strongly graded ring, Leavitt path algebra
National Category
Mathematics
Research subject
ENGINEERING, Mathematics
Identifiers
URN: urn:nbn:se:hv:diva-14470DOI: 10.1142/S0219498820501650Scopus ID: 2-s2.0-85071375607OAI: oai:DiVA.org:hv-14470DiVA, id: diva2:1357063
Available from: 2019-10-02 Created: 2019-10-02 Last updated: 2019-11-12Bibliographically approved

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Nystedt, Patrik

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