Complex Nilpotent Structures in Soluble Lie Algebras

Authors

  • Jaqueline Alexsandra Azevedo Ferreira UFRB

Keywords:

Nilpotent s-steps complex structure, Lie algebra, Brakets

Abstract

Considering a Lie Algebra (g, [.,.]) With complex J structure, it is possible to define a new Lie bracket in g Considering a Lie Algebra g, [.,.] With complex structure J, it is possible to define in g a new Lie bracket, so that it can be shown that the subspaces g1,0 and g0,1 are sub-algebras of Lie isomorphic ag, [*]. For that, we only consider complex integrable structures. We will show that if these sub-algebras are nilpotent, then (g, [.,.]) It will be soluble. In this sense, a characterization of the Lie Algebras (g, [*] J) with a nilpotent s-step complex structure will be made, in order to study the behavior of the original Lie bracket [.,.], Thus allowing the construction of examples of Lie algebras of dim = 6.

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Published

2020-12-15

How to Cite

Azevedo Ferreira, J. A. (2020). Complex Nilpotent Structures in Soluble Lie Algebras. Electronic Journal of Exact and Technological Sciences, 1(1). Retrieved from https://www3.ufrb.edu.br/index.php/recet/article/view/1347

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Section

Mathematics

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