Abstract
In this paper, we continue the study of the infinitesimal deformations of the Lie superalgebra L n , 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 ( S 2 ( L 1 n , m ) , L 0 n , 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 ( S 2 ( L 1 n , m ) , L 0 n , 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 .
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