Quadratic symplectic Lie superalgebras with a filiform module as an odd part

Abstract

The present work studies deeply quadratic symplectic Lie superalgebras, obtaining, in particular, that they are all nilpotent. Consequently, we provide classifications in low dimensions and identify the double extensions that maintain symplectic structures. By means of both elementary odd double extensions and generalized double extensions of quadratic symplectic Lie superalgebras, we obtain an inductive description of quadratic symplectic Lie superalgebras of filiform type.

Odd-quadratic Lie superalgebras with a weak filiform module as an odd part

“…In [3] we studied the class of quadratic Lie superalgebras g = g0 ⊕ g1 such that g1 is a filiform g0-module (to short we called filiform type). We showed that the study of quadratic Lie superalgebras of filiform type can be reduced to those that are solvable.…”