On indecomposable solvable Lie superalgebras having a Heisenberg nilradical

Author:

Rodríguez-Vallarte M. C.1,Salgado G.1,Sánchez-Valenzuela O. A.2

Affiliation:

1. Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, Av. Salvador Nava s/n, Zona Universitaria, S.L.P., San Luis Potosí C.P. 78290, México

2. Centro de Investigación en Matemáticas, Jalisco S/N, Col. Valenciana, Guanajuato, Gto. C.P. 36000, México

Abstract

All solvable, indecomposable, finite-dimensional, complex Lie superalgebras [Formula: see text] whose first derived ideal lies in its nilradical, and whose nilradical is a Heisenberg Lie superalgebra [Formula: see text] associated to a [Formula: see text]-homogeneous supersymplectic complex vector superspace [Formula: see text], are here classified up to isomorphism. It is shown that they are all of the form [Formula: see text], where [Formula: see text] is even and consists of non-[Formula: see text]-nilpotent elements. All these Lie superalgebras depend on an element [Formula: see text] in the dual space [Formula: see text] and on a pair of linear maps defined on [Formula: see text], and taking values in the Lie algebras naturally associated to the even and odd subspaces of [Formula: see text]; namely, if the supersymplectic form is even, the pair of linear maps defined on [Formula: see text] take values in [Formula: see text], and [Formula: see text], respectively, whereas if the supersymplectic form is odd these linear maps take values on [Formula: see text]. When the supersymplectic form is even, a bilinear, skew-symmetric form defined on [Formula: see text] is further needed. Conditions on these building data are given and the isomorphism classes of the resulting Lie superalgebras are described in terms of appropriate group actions.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

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