The aim of this paper is to compute and discuss the index of Lie algebras. We consider the n-dimensional Lie algebras for n < 5 and the case of filiform Lie algebras which form a special class of nilpotent Lie algebras. We compute the index of generalized Heisenberg algebras and graded filiform Lie algebras Ln and Qn. We also discuss the evolution of the Lie algebra index by deformation.
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