Computer-Aided Study of Double Extensions of Restricted Lie Superalgebras Preserving the Nondegenerate Closed 2-Forms in Characteristic 2

Abstract

A Lie (super)algebra with a nondegenerate invariant symmetric bilinear form B is called a nis-(super)algebra. The double extension of a nis-(super)algebra is the result of simultaneous adding to a central element and a derivation so that is a nis-algebra. Loop algebras with values in simple complex Lie algebras are most known among the Lie (super)algebras suitable to be doubly extended. In characteristic 2, the notion of double extension acquires specific features. Restricted Lie (super)algebras are among the most interesting modular Lie superalgebras. In characteristic 2, using Grozman’s Mathematica-based package SuperLie, we list double extensions of restricted Lie superalgebras preserving the nondegenerate closed 2-forms with constant coefficients. The results are proved for the number of indeterminates ranging from 4 to 7—sufficient to conjecture the pattern for larger numbers. Considering multigradings allowed us to accelerate computations up to 100 times.