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

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.

17 pages

References in corpus (2)

• n-ary algebras: a review with applications
• Operads for n-ary algebras - calculations and conjectures

Cited by in corpus (1)

• Cartan class of Invariant forms on Lie groups