ArticleOriginal scientific text
Title
Formal differential geometry and Nambu-Takhtajan algebra
Authors 1, 1
Affiliations
- National Technical University of Ukraine, 37 Peremogy prosp., Kiev, Ukraine
Bibliography
- I. M. Gelfand and Yu. L. Daletsky, Lie Superalgebras and Hamiltonian Operators. Rep. No. 16 Sem. Supermanifolds, Dept. Math. Univ. Stockholm, 1987, 26 p.
- I. M. Gelfand, Yu. L. Daletskii and B. L. Tsygan, On a Variant of Non-Commutative Differential Geometry. Soviet Math. Dokl. 40 (1990), 2, 422-426.
- I. M. Gelfand and I. Ya. Dorfman, Hamiltonian operators and algebraic structures connected with them. Funct. anal. appl. 13 (1979), 4, 13-30.
- I. M. Gelfand and I. Ya. Dorfman, Hamiltonian operators and infinite dimensional Lie algebras. Funct. anal. appl. 15 (1981), 3, 23-40.
- M. Dubois-Violette, R. Kerner and J. Madore, Noncommutative Differential Geometry of Matrix Algebras. J. Math. Phys. 31 (1990), 2, 316-322.
- Yu. L. Daletskii and B. L. Tsygan, Operations on Hochschild and Cyclic Complexes.
-Theorie, (in print). - Yu. L. Daletskii and B. L. Tsygan, Hamoltonian Operators and Hochschild Homology. Funct. anal. appl. 19 (1985), 4, 82-83.
- A. Cabras and A. M. Vinogradov, Extension of the Poisson Bracket to Differential Forms and Multi-Vector Fields. J. Geom. and Physics, 9 (1992), 75-100.
- Yu. L. Daletskii and V. A. Kushnirevitch, Poisson and Nijenhuis Brackets for Differential Forms on Non-Commutative Manifold. SFB 237 - Preprint Nr 274, Institut für Mathemetik, Ruhr-Universität-Bochum, September, 1995. 29 p.
- Y. Nambu, Generalized Hamiltonian Dynamics. Phys. Review D7 (1973), 8, 2405-2412.
- L. Takhtajan, On Foundation of the Generalized Nambu Mechanics. Commun. Math. Phys. 160 (1994), 295-315.
- L. Takhtajan, Higher Order Analog of Chevalley-Eilenberg Complex and Deformation theory of
-gebras. Algebra and Analysis, 6 (1994), 2, 262-272. - Yu. L. Daletskii, Hamiltonian Operators in Graded Formal Calculus of Variations. Funct. anal. appl. 20 (1986), 2, 62-64.
- B. A. Kupershmidt, Elements of Superintegrable Systems. Reidel, 1987.
- A. Connes, Géométrie Non Commutative. InterEditions, 1990.
- S. L. Woronowicz, Differential Calculus on Compact Matrix Pseudogroups (Quantum Groups). Commun. Math. Phys. 122 (1989), 125-170.