On the classification of 3-dimensional complex hom-Lie algebras

2019/10/29 by Edison Alberto Fernández-Culma, Fernández-Culma, Edison Alberto, Nadina Rojas +1
Mathematics · #17B99 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1910.13528

openalex publication_date 2019/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify hom-Lie structures with nilpotent twisting map on 3-dimensional complex Lie algebras, up to isomorphism, and classify all degenerations in such family. The ideas and techniques presented here can be easily extrapolated to study similar problems in other algebraic structures and provide different perspectives from where one can tackle classical open problems of interest in rigid Lie algebras.

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