On isomorphism criteria for Leibniz central extensions of a linear deformation of mu_n.

This paper deals with the classification problems of Leibniz central extensions of linear deformations of a Lie algebra. It is known that any n-dimensional filiform Lie algebra can be represented as a linear deformation of n-dimensional filiform Lie algebra μ n given by the brackets [e i, e 0] = e i+1, i = 0,1,⋯,n-2, in a basis {e 0, e 1,⋯,e n-1}. In this paper we consider a linear deformation of μ n and its Leibniz central extensions. The resulting algebras are Leibniz algebras, this class is denoted here by Ced(μ n). We choose an appropriate basis of Ced(μ n) and give general isomorphism criteria. By using the isomorphism criteria, one can classify the class Ced(μ n) for any fixed n. Two relevant maple programs are provided.

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