Kushnirevych V. Leibniz Superalgebras and their Application

The dissertation is devoted to investigation of Leibniz superalgebra. The analog of (A,D)-sytem in the case A being Leibniz superalgebra is built and Abelian extension of Leibniz superalgebra is studied. Using new notation of multimodule and multicomplex Nambu superalgebra is investigated concerning to (A,D)-system theory. New examples of Poisson brackets are introduced. Universal method to construct Poisson bracket for differential forms, vectorvalued differential forms, multivector fields, etc, is given. New examples of Nambu superalgebras are found (generalized jacobians). Certain class of Hamiltonian elements in formal calculus of variations theory is described.