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

Yuval Ginosar; Ofir Schnabel

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

Rings and Algebras 2013-05-22 v1 Combinatorics

Authors: Yuval Ginosar , Ofir Schnabel

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 $\Gamma =(V,E)$ without parallel edges, and deduce that for any simple group-grading, the dimension of the trivial component is maximal.

Keywords

simply-graded algebras digraphs dimension trivial component group-grading

Cite

@article{arxiv.1305.4749,
  title  = {A graph-theoretic approach for comparing dimensions of components in simply-graded algebras},
  author = {Yuval Ginosar and Ofir Schnabel},
  journal= {arXiv preprint arXiv:1305.4749},
  year   = {2013}
}

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

Abstract

Keywords

Cite

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