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A graph-theoretic approach for comparing dimensions of components in simply-graded algebras
Authors:Yuval Ginosar  Ofir Schnabel
Affiliation:Department of Mathematics, University of Haifa, Haifa 3498838, Israel
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.
Keywords:Mutually neighbored vertices   Simply-graded algebras
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