Poisson and Hamiltonian Superpairs over Polarized Associative Algebras

Details Poisson and Hamiltonian Superpairs over Polarized Associative Algebras Poisson and Hamiltonian Superpairs over Polarized Associative Algebras

2000-10-08

arxiv.org/abs/math/0010074v2

Mathematics

Quantum Algebra

30 pages, Latex file

Scientific paper

Poisson superpair is a pair of Poisson superalgebra structures on a super commutative associative algebra, whose any linear combination is also a Poisson superalgebra structure. In this paper, we first construct certain linear and quadratic Poisson superpairs over a finite-dimensional or semi-finitely-filtered polarized $\Bbb{Z}_2$-graded associative algebra. Then we give a construction of certain Hamiltonian superpairs in the formal variational calculus over any finite-dimensional $\Bbb{Z}_2$-graded associative algebra with a supersymmetric nondegenerate associative bilinear form. Our constructions are based on the Adler mapping in a general sense. Our works in this paper can be viewed as noncommutative generalizations of the Adler-Gel'fand-Dikii Hamiltonian pair. As a preparatory work, some structural properties of polarized associative algebras have been studied.

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