Classifying good gradings on structural matrix algebras

Let k be a field and let be a partial order on the set . If G is a group, we classify the good G-gradings on the associated structural matrix algebra as the orbits of the action of the automorphism group of on a certain set of functions. We explicitly count the number of isomorphism types of good gr...

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Bibliographic Details
Published in:Linear & multilinear algebra 2019-10, Vol.67 (10), p.1948-1957
Main Authors: Beşleagă, F., Dăscălescu, S., Van Wyk, L.
Format: Article
Language:English
Subjects:
Automorphisms
Classification
directed graph
group graded algebra
Isomorphism
Mathematical analysis
Matrix algebra
orbits of a group action
poset
structural matrix algebra
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Summary:Let k be a field and let be a partial order on the set . If G is a group, we classify the good G-gradings on the associated structural matrix algebra as the orbits of the action of the automorphism group of on a certain set of functions. We explicitly count the number of isomorphism types of good gradings in some cases where G is finite and the graph associated with has a cyclic associated undirected graph.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2018.1476447