https://www.mdu.se/

mdu.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Induced Ternary Hom-Nambu-Lie algebras
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. University of Nairobi; Kenya. (MAM)ORCID iD: 0000-0003-3468-5282
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)
University of Nairobi, Kenya.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0003-4554-6528
(English)Manuscript (preprint) (Other academic)
Abstract [en]

This study is concerned with induced ternary Hom-Lie-Nambu Lie algebras from Hom-Lie algebras and their classification. The induced algebras are constructed from a class of Hom-Lie algebra with nilpotent linear map. The families of ternary Hom-Nambu-Lie arising in this way of construction are classified for a given  class of  nilpotent linear maps. In addition, some results giving conditions on when morphisms of Hom-Lie algebras can still remain morphisms for the induced ternary Hom-Nambu-Lie algebras are given.

National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-55882OAI: oai:DiVA.org:mdh-55882DiVA, id: diva2:1594255
Available from: 2021-09-15 Created: 2021-09-15 Last updated: 2022-01-04Bibliographically approved
In thesis
1. Classification and Construction of Low-dimensional Hom-Lie Algebras and Ternary Hom-Nambu-Lie Algebras
Open this publication in new window or tab >>Classification and Construction of Low-dimensional Hom-Lie Algebras and Ternary Hom-Nambu-Lie Algebras
2021 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis concerns the construction and classification of low-dimensional Hom-Lie algebras and ternary Hom-Nambu-Lie algebras. A classification of 3-dimensional Hom-Lie algebras is given for nilpotent linear endomorphism, as a twisting map, and a construction of 4-dimensional Hom-Lie algebras is done. Results on the dimension of the space of endomorphisms that turn a skew-symmetric algebra into a Hom-Lie algebra are also given in this thesis. A class of 3-dimensional ternary Hom-Nambu-Lie algebras with nilpotent linear maps are constructed and classified.

In Chapter 2, we derive conditions for an arbitrary n-dimensional algebra to be a Hom-Lie algebra, in the form of a system of polynomial equations, containing both structure constants of the skew-symmetric bilinear map and constants describing the twisting linear endomorphism. When the algebra is 3 or 4-dimensional, we describe the realisation of Hom-Lie algebras when the dimension of the space of such linear endomorphisms, as vector spaces, is minimum. For the 3-dimensional case we give all possible families of 3-dimensional Hom-Lie algebras arising from a general nilpotent linear endomorphism constructed up to isomorphism together with non-isomorphic canonical representatives for all the families in that case. We further give a list of 4-dimensional Hom-Lie algebras arising from general nilpotent linear endomorphisms.

In Chapter 3, we describe the dimension of the space of possible linear endomorphisms that turn skew-symmetric three-dimensional algebras into Hom-Lie algebras. We find a correspondence between the rank of a matrix containing the structure constants of the bilinear product and the dimension of the space of Hom-Lie structures. Examples from classical complex Lie algebras are given to demonstrate this correspondence.

In Chapter 4, the space of possible Hom-Lie structures on complex 4-dimensional Lie algebras is considered in terms of linear maps that turn the Lie algebras into Hom-Lie algebras. Hom-Lie structures and automorphism groups on the representatives of isomorphism classes of complex 4-dimensional Lie algebras are described.

In Chapter 5, we construct ternary Hom-Nambu-Lie algebras from Hom-Lie algebras through a process known as induction. The induced algebras are constructed from a class of Hom-Lie algebra with nilpotent linear map. The families of ternary Hom-Nambu-Lie arising in this way of construction are classified for a given class of nilpotent linear maps. In addition, some results giving conditions on when morphisms of Hom-Lie algebras can still remain morphisms for the induced ternary Hom-Nambu-Lie algebras are given. 

Place, publisher, year, edition, pages
Västerås: Mälardalen University, 2021
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 345
National Category
Natural Sciences
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-55920 (URN)978-91-7485-523-4 (ISBN)
Public defence
2021-10-29, Delta & zoom, Mälardalens högskola, Västerås, 15:15 (English)
Opponent
Supervisors
Available from: 2021-09-17 Created: 2021-09-16 Last updated: 2021-10-08Bibliographically approved

Open Access in DiVA

No full text in DiVA

Authority records

Ongong'A, ElviceKitouni, AbdennourSilvestrov, Sergei

Search in DiVA

By author/editor
Ongong'A, ElviceKitouni, AbdennourSilvestrov, Sergei
By organisation
Educational Sciences and Mathematics
Algebra and Logic

Search outside of DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric score

urn-nbn
Total: 214 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf