Formal differential geometry and Nambu-Takhtajan algebra

• Autorzy: Yuri L. Daletskii , Vitaly A. Kushnirevitch
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1997
• Tom: 40
• Numer: 1
• Strony: 293-302

Daty

wydano

1997

Twórcy

autor

Yuri L. Daletskii

• National Technical University of Ukraine, 37 Peremogy prosp., Kiev, Ukraine

autor

Vitaly A. Kushnirevitch

• National Technical University of Ukraine, 37 Peremogy prosp., Kiev, Ukraine

Bibliografia

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• [2] 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.
• [3] I. M. Gelfand and I. Ya. Dorfman, Hamiltonian operators and algebraic structures connected with them. Funct. anal. appl. 13 (1979), 4, 13-30.
• [4] I. M. Gelfand and I. Ya. Dorfman, Hamiltonian operators and infinite dimensional Lie algebras. Funct. anal. appl. 15 (1981), 3, 23-40.
• [5] M. Dubois-Violette, R. Kerner and J. Madore, Noncommutative Differential Geometry of Matrix Algebras. J. Math. Phys. 31 (1990), 2, 316-322.
• [6] Yu. L. Daletskii and B. L. Tsygan, Operations on Hochschild and Cyclic Complexes. $K$-Theorie, (in print).
• [7] Yu. L. Daletskii and B. L. Tsygan, Hamoltonian Operators and Hochschild Homology. Funct. anal. appl. 19 (1985), 4, 82-83.
• [8] 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.
• [9] 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.
• [10] Y. Nambu, Generalized Hamiltonian Dynamics. Phys. Review D7 (1973), 8, 2405-2412.
• [11] L. Takhtajan, On Foundation of the Generalized Nambu Mechanics. Commun. Math. Phys. 160 (1994), 295-315.
• [12] L. Takhtajan, Higher Order Analog of Chevalley-Eilenberg Complex and Deformation theory of $N$-gebras. Algebra and Analysis, 6 (1994), 2, 262-272.
• [13] Yu. L. Daletskii, Hamiltonian Operators in Graded Formal Calculus of Variations. Funct. anal. appl. 20 (1986), 2, 62-64.
• [14] B. A. Kupershmidt, Elements of Superintegrable Systems. Reidel, 1987.
• [15] A. Connes, Géométrie Non Commutative. InterEditions, 1990.
• [16] S. L. Woronowicz, Differential Calculus on Compact Matrix Pseudogroups (Quantum Groups). Commun. Math. Phys. 122 (1989), 125-170.