Odd Jacobi Manifolds and Loday-Poisson Brackets
We construct a nonskew symmetric version of a Poisson bracket on the algebra of smooth functions on an odd Jacobi supermanifold. We refer to such Poisson-like brackets as Loday-Poisson brackets. We examine the relations between the Hamiltonian vector fields with respect to both the odd Jacobi struct...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/630749 |
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| _version_ | 1832559085273219072 |
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| author | Andrew James Bruce |
| author_facet | Andrew James Bruce |
| author_sort | Andrew James Bruce |
| collection | DOAJ |
| description | We construct a nonskew symmetric version of a Poisson bracket on the algebra of smooth functions on an odd Jacobi supermanifold. We refer to such Poisson-like brackets as Loday-Poisson brackets. We examine the relations between the Hamiltonian vector fields with respect to both the odd Jacobi structure and the Loday-Poisson structure. Furthermore, we show that the Loday-Poisson bracket satisfies the Leibniz rule over the noncommutative product derived from the homological vector field. |
| format | Article |
| id | doaj-art-86252e433d4b41f48d0eac152ef43e14 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-86252e433d4b41f48d0eac152ef43e142025-02-03T01:30:53ZengWileyJournal of Mathematics2314-46292314-47852014-01-01201410.1155/2014/630749630749Odd Jacobi Manifolds and Loday-Poisson BracketsAndrew James Bruce0Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 21, 00-956 Warszawa, PolandWe construct a nonskew symmetric version of a Poisson bracket on the algebra of smooth functions on an odd Jacobi supermanifold. We refer to such Poisson-like brackets as Loday-Poisson brackets. We examine the relations between the Hamiltonian vector fields with respect to both the odd Jacobi structure and the Loday-Poisson structure. Furthermore, we show that the Loday-Poisson bracket satisfies the Leibniz rule over the noncommutative product derived from the homological vector field.http://dx.doi.org/10.1155/2014/630749 |
| spellingShingle | Andrew James Bruce Odd Jacobi Manifolds and Loday-Poisson Brackets Journal of Mathematics |
| title | Odd Jacobi Manifolds and Loday-Poisson Brackets |
| title_full | Odd Jacobi Manifolds and Loday-Poisson Brackets |
| title_fullStr | Odd Jacobi Manifolds and Loday-Poisson Brackets |
| title_full_unstemmed | Odd Jacobi Manifolds and Loday-Poisson Brackets |
| title_short | Odd Jacobi Manifolds and Loday-Poisson Brackets |
| title_sort | odd jacobi manifolds and loday poisson brackets |
| url | http://dx.doi.org/10.1155/2014/630749 |
| work_keys_str_mv | AT andrewjamesbruce oddjacobimanifoldsandlodaypoissonbrackets |