Abstract
A Poisson superpair is a pair of Poisson superalgebra structures on a supercommutative 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 2-graded associative algebra. Then we give a construction of certain Hamiltonian superpairs in the formal variational calculus over any finite-dimensional 2-graded associative algebra with a supersymmetric nondegenerate associative bilinear form. Our constructions are based on the Adler mapping in a general sense. Our results in this paper can be viewed as noncommutative generalizations of the Adler–Gel'fand–Dikii Hamiltonian pair.
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