Variational calculus of supervariables and related algebraic structures

Details Variational calculus of supervariables and related algebraic structures Variational calculus of supervariables and related algebraic structures

1999-11-24

arxiv.org/abs/math/9911191v1

Mathematics

Quantum Algebra

32pages,Latex;To appear in journal of Algebra; Preprint was circulated in a certain mathematical community in January 1995

Scientific paper

We establish a formal variational calculus of supervariables, which is a combination of the bosonic theory of Gel'fand-Dikii and the fermionic theory in our earlier work. Certain interesting new algebraic structures are found in connection with Hamiltonian superoperators in terms of our theory. In particular, we find connections between Hamiltonian superoperators and Novikov-Poisson algebras that we introduced in our earlier work in order to establish a tensor theory of Novikov algebras. Furthermore, we prove that an odd linear Hamiltonian superoperator in our variational calculus induces a Lie superalgebra, which is a natural generalization of the Super-Virasoro algebra under certain conditions.

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