Lie algebras with associative structures. Applications to the study of 2-step nilpotent Lie algebras

2012/01/12 by Goze, Michel, Remm, Elisabeth
#16W10 #17B25 #18D50 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1201.2674

Abstract

We investigate Lie algebras whose Lie bracket is also an associative or cubic associative multiplication to characterize the class of nilpotent Lie algebras with a nilindex equal to 2 or 3. In particular we study the class of 2-step nilpotent Lie algebras, their deformations and we compute the cohomology which parametrize the deformations in this class.

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