Poisson and Hamiltonian Superpairs over Polarized Associative Algebras
| dc.creator | Xu, Xiaoping | |
| dc.date | 2000-10-08 | |
| dc.date | 2001-01-31 | |
| dc.date.accessioned | 2026-07-07T04:37:54Z | |
| dc.date.available | 2026-07-07T04:37:54Z | |
| dc.description | 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. | |
| dc.description | 30 pages, Latex file | |
| dc.identifier | https://arxiv.org/abs/math/0010074 | |
| dc.identifier | http://arxiv.org/abs/math/0010074 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60076 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Mathematical Physics | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 58F05, 35Q58 | |
| dc.title | Poisson and Hamiltonian Superpairs over Polarized Associative Algebras | |
| dc.type | text |