Poisson and Hamiltonian Superpairs over Polarized Associative Algebras1
نویسنده
چکیده
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 semi-finitely-filtered polarized Z2-graded associative algebra. Then we give a construction of certain Hamiltonian superpairs in the formal variational calculus over any finite-dimensional Z2-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.
منابع مشابه
Polarized Associative Algebras1
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 Z2-graded associative algebra. Then we give a construction of certain Hamil...
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