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Group gradations on Leavitt path algebras.
- Source :
-
Journal of Algebra & Its Applications . Sep2020, Vol. 19 Issue 9, pN.PAG-N.PAG. 16p. - Publication Year :
- 2020
-
Abstract
- Given a directed graph E and an associative unital ring R one may define the Leavitt path algebra with coefficients in R , denoted by L R (E). For an arbitrary group G , L R (E) can be viewed as a G -graded ring. In this paper, we show that L R (E) is always nearly epsilon-strongly G -graded. We also show that if E is finite, then L R (E) is epsilon-strongly G -graded. We present a new proof of Hazrat's characterization of strongly ℤ -graded Leavitt path algebras, when E is finite. Moreover, if E is row-finite and has no source, then we show that L R (E) is strongly ℤ -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 L R (E) is Frobenius over its identity component. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGEBRA
*ASSOCIATIVE rings
*DIRECTED graphs
Subjects
Details
- Language :
- English
- ISSN :
- 02194988
- Volume :
- 19
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 145186240
- Full Text :
- https://doi.org/10.1142/S0219498820501650