Nonlinear realizations of Lie superalgebras

Abstract

For any decomposition of a Lie superalgebra into a direct sum of a subalgebra and a subspace without any further resctrictions on and we construct a nonlinear realization of on The result generalizes a theorem by Kantor from Lie algebras to Lie superalgebras. When is a differential graded Lie algebra, we show that it gives a construction of an associated -algebra.