Publication: Completeness of low-dimensional leibniz algebras
2
0
Issued Date
2024-03-01
Resource Type
ISSN
16860209
Scopus ID
2-s2.0-85191376556
Journal Title
Thai Journal of Mathematics
Volume
22
Issue
1
Start Page
165
End Page
178
Rights Holder(s)
SCOPUS
Bibliographic Citation
Thai Journal of Mathematics Vol.22 No.1 (2024) , 165-178
Suggested Citation
Kongsomprach Y., Pongprasert S., Rungratgasame T., Tiansa-Ard S. Completeness of low-dimensional leibniz algebras. Thai Journal of Mathematics Vol.22 No.1 (2024) , 165-178. 178. Retrieved from: https://hdl.handle.net/20.500.14740/20267
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Abstract
Leibniz algebras are generalizations of Lie algebras. By using the classification results of low-dimensional non-Lie nilpotent and non-nilpotent solvable Leibniz algebras obtained earlier, we define a basis of the derivation algebra Der(A) of each Leibniz algebra A and study their properties. It is known that for a Leibniz algebra A if the Lie algebra A/ Leib(A) is complete, then A is a complete Leibniz algebra. We show that the converse holds when A is a complete solvable Leibniz algebra with dim(A) ≤ 3. It is also known that for the derivation algebra of a complete Lie algebra is complete. However, our results show that this is not true for Leibniz algebras.