Journal
LINEAR & MULTILINEAR ALGEBRA
Volume 67, Issue 7, Pages 1471-1482Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/03081087.2018.1457622
Keywords
Lie algebra; Leibniz algebra; semisimple algebra; solvable radical; Levi-Malcev decomposition; inner automorphism
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Funding
- Agencia Estatal de Investigacion (Spain) [MTM2016-79661-P]
- Ministry of Education and Science of the Republic of Kazakhstan [0828/GF4]
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The present paper is devoted to provide conditions for the Levi-Malcev theorem to hold or not to hold (i.e. for two Levi subalgebras to be or not conjugate by an inner automorphism) in the context of finite-dimensional Leibniz algebras over a field of characteristic zero. Particularly, in the case of the field C of complex numbers, we consider all possible cases in which Levi subalgebras are conjugate and not conjugate.
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