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Group gradations on Leavitt path algebras
Högskolan Väst, SWE.
Blekinge Tekniska Högskola, Fakulteten för teknikvetenskaper, Institutionen för matematik och naturvetenskap.ORCID-id: 0000-0001-8095-0820
2019 (engelsk)Inngår i: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
World Scientific Publishing Co. Pte Ltd , 2019.
Emneord [en]
epsilon-strongly graded ring, Leavitt path algebra, S-Unital ring, strongly graded ring
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Identifikatorer
URN: urn:nbn:se:bth-18645DOI: 10.1142/S0219498820501650Scopus ID: 2-s2.0-85071375607OAI: oai:DiVA.org:bth-18645DiVA, id: diva2:1350551
Tilgjengelig fra: 2019-09-11 Laget: 2019-09-11 Sist oppdatert: 2019-09-11bibliografisk kontrollert

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