A graph-theoretic approach for comparing dimensions of components in simply-graded algebras |
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Authors: | Yuval Ginosar Ofir Schnabel |
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Affiliation: | Department of Mathematics, University of Haifa, Haifa 3498838, Israel |
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Abstract: | Any simple group-grading of a finite dimensional complex algebra induces a natural family of digraphs. We prove that in a digraph without parallel edges, the number of pairs of vertices having a common in-neighbor or a common out-neighbor is at least the number of edges. We deduce that for any simple group-grading, the dimension of the trivial component is maximal. |
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Keywords: | Mutually neighbored vertices Simply-graded algebras |
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