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Linear and Multilinear Algebra Volume 70, 2022 - Issue 1
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Original Articles

Degenerations of graph Lie algebras

B. Alfaro Arancibiaa Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta, ChileView further author information
,
M. A. Alvareza Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta, ChileCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-2221-2325View further author information
ORCID Icon &
Y. Anzab Facultad de Educación, Universidad de Antofagasta, Antofagasta, ChileView further author information
Pages 91-100 | Received 26 Apr 2019, Accepted 02 Jan 2020, Published online: 13 Jan 2020
 
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Abstract

In this work we associate a Lie algebra to every finite simple graph and obtain a necessary and sufficient condition for the existence of degenerations between these Lie algebras. As a corollary, we obtain that all these algebras belong to the irreducible component within the variety of 2-step nilpotent Lie algebras, given by the orbit closure of the free 2-step nilpotent Lie algebra.

2010 Mathematics Subject Classifications:

Disclosure statement

No potential conflict of interest was reported by the authors.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

B. Alfaro-Arancibia and Y. Anza were supported by MINEDUC-UA project, code ANT 1856. B. Alfaro-Arancibia also thanks the Magíster en Cien mención Matemática Aplicada from Universidad de Antofagasta. M. A. Alvarez was supported by “Fondo Puente de Investigación de Excelencia” FPI-18-02 from Universidad de Antofagasta.

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