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Classification of 3-dimensional Hom-Lie algebras
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. University of Nairobi, Nairobi, Kenya .
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.ORCID iD: 0000-0003-3931-7358
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.ORCID iD: 0000-0003-4554-6528
2019 (English)In: Journal of Physics: Conference Series, Institute of Physics Publishing , 2019, no 1Conference paper, Published paper (Refereed)
Abstract [en]

For any n-dimensional Hom-Lie algebra, a system of polynomial equations is obtained from the Hom-Jacobi identity, containing both structure constants of the skew-symmetric bilinear map and constants describing the twisting linear endomorphism. The equations are linear in the constants representing the endomorphism and non-linear in the structure constants. The space of possible endomorphisms has minimum dimension 6, and we describe the possible endomorphisms in that case. We further give families of 3-dimensional Hom-Lie algebras arising from a general nilpotent linear endomorphism constructed upto isomorphism.

Place, publisher, year, edition, pages
Institute of Physics Publishing , 2019. no 1
Keywords [en]
Polynomials, 3-dimensional, Bilinear map, Lie Algebra, Nilpotent, Non linear, Skew-symmetric, Structure constants, System of polynomial equations, Group theory
National Category
Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-43500DOI: 10.1088/1742-6596/1194/1/012084Scopus ID: 2-s2.0-85065590036OAI: oai:DiVA.org:mdh-43500DiVA, id: diva2:1322947
Conference
32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018, 9 July 2018 through 13 July 2018
Note

Conference code: 147785; Export Date: 24 May 2019; Conference Paper

Available from: 2019-06-11 Created: 2019-06-11 Last updated: 2019-06-11Bibliographically approved

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Ongong'A, ElviceRichter, JohanSilvestrov, Sergei

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CiteExportLink to record
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  • apa
  • ieee
  • modern-language-association-8th-edition
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  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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Output format
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