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

Yuval Ginosar; Ofir Schnabel

doi:10.1016/j.disc.2014.08.018

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

Yuval Ginosar
, Ofir Schnabel

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	59-63
Number of pages	5
Journal	Discrete Mathematics
Volume	338
DOIs	https://doi.org/10.1016/j.disc.2014.08.018
State	Published - 6 Jan 2015

Bibliographical note

Publisher Copyright:
© 2014 Elsevier B.V.

Keywords

Mutually neighbored vertices
Simply-graded algebras

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2014.08.018

Cite this

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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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KW - Simply-graded algebras

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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