A graph-theoretic approach for comparing dimensions of components in simply-graded algebras

Yuval Ginosar; Ofir Schnabel

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arXiv · 1305.4749

A graph-theoretic approach for comparing dimensions of components in simply-graded algebras

Yuval Ginosar·Ofir Schnabel

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Abstract

Any simple group-grading of a finite dimensional complex algebra induces a natural family of digraphs. We prove that $|E\circ E^{\text{op}}\cup E^{\text{op}}\circ E|\geq |E|$ for any digraph $Γ=(V,E)$ without parallel edges, and deduce that for any simple group-grading, the dimension of the trivial component is maximal.

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Yuval Ginosar, Ofir Schnabel. 2013-05-21. A graph-theoretic approach for comparing dimensions of components in simply-graded algebras. https://arxiv.org/abs/1305.4749

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