Thursday, 15 September 2016

Generalizing Two Structure Theorems of Lie Algebras to the Fuzzy Lie Algebras

Lie algebras were proposed by Sophus Lie and there are many applications of them in several branches of physics. The notion of fuzzy sets was introduced by Zadeh and manymathematicians have been involved in extending the concepts and results ofabstract Lie algebra to fuzzy theory. 

Lie Algebras
This paper is the continuation of the results obtained in, where we presented conditions to generalize the concepts of solvable and nilpotent radicals of Lie algebras (called of solvable and nilpotent fuzzy radicals, respectively) to a class of fuzzy Lie algebras. Inthis article we use the solvable fuzzy radical to generalize the structuretheorem of semisimple Lie algebras and the Levi’s decomposition theorem to aclass of the fuzzy Lie algebras. The results presented in this paper are still strongly connected with results proved in.

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