Infinitesimal deformations of the Lie superalgebra Ln,m

Abstract

In this paper, we continue the study of the infinitesimal deformations of the Lie superalgebra Ln, m that we have started in [M. Bordemann, J.R. Gómez, Yu. Khakimdjanov, R.M. Navarro, Some deformations of nilpotent Lie superalgebras, J. Geom. Phys. 57 (2007) 1391-1403]. These deformations allow us to obtain all filiform Lie superalgebras. In [M. Bordemann, J.R. Gómez, Yu. Khakimdjanov, R.M. Navarro, Some deformations of nilpotent Lie superalgebras, J. Geom. Phys. 57 (2007) 1391-1403], we gave a method that allows us to determine the dimension of the space of deformations of type Hom (S2 (L1n, m), L0n, m) and we calculated a basis of the aforementioned space of deformations for n ≥ 2 m - 1. In this paper, we conclude the study by developing a method to calculate a basis of the space of deformations Hom (S2 (L1n, m), L0n, m) for the rest of possibilities n < 2 m - 1. We particularize for even n and also give an algorithm for computing a cocycle basis for the given concrete dimensions n and m. © 2008 Elsevier B.V. All rights reserved.