Formal differential geometry and Nambu-Takhtajan algebra

Yuri Daletskii; Vitaly Kushnirevitch

Banach Center Publications (1997)

  • Volume: 40, Issue: 1, page 293-302
  • ISSN: 0137-6934

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Daletskii, Yuri, and Kushnirevitch, Vitaly. "Formal differential geometry and Nambu-Takhtajan algebra." Banach Center Publications 40.1 (1997): 293-302. <http://eudml.org/doc/252226>.

@article{Daletskii1997,
author = {Daletskii, Yuri, Kushnirevitch, Vitaly},
journal = {Banach Center Publications},
keywords = {graded Lie algebra; de Rham complex},
language = {eng},
number = {1},
pages = {293-302},
title = {Formal differential geometry and Nambu-Takhtajan algebra},
url = {http://eudml.org/doc/252226},
volume = {40},
year = {1997},
}

TY - JOUR
AU - Daletskii, Yuri
AU - Kushnirevitch, Vitaly
TI - Formal differential geometry and Nambu-Takhtajan algebra
JO - Banach Center Publications
PY - 1997
VL - 40
IS - 1
SP - 293
EP - 302
LA - eng
KW - graded Lie algebra; de Rham complex
UR - http://eudml.org/doc/252226
ER -

References

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  1. [1] I. M. Gelfand and Yu. L. Daletsky, Lie Superalgebras and Hamiltonian Operators. Rep. No. 16 Sem. Supermanifolds, Dept. Math. Univ. Stockholm, 1987, 26 p. 
  2. [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. [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. [4] I. M. Gelfand and I. Ya. Dorfman, Hamiltonian operators and infinite dimensional Lie algebras. Funct. anal. appl. 15 (1981), 3, 23-40. 
  5. [5] M. Dubois-Violette, R. Kerner and J. Madore, Noncommutative Differential Geometry of Matrix Algebras. J. Math. Phys. 31 (1990), 2, 316-322. Zbl0704.53081
  6. [6] Yu. L. Daletskii and B. L. Tsygan, Operations on Hochschild and Cyclic Complexes. K -Theorie, (in print). 
  7. [7] Yu. L. Daletskii and B. L. Tsygan, Hamoltonian Operators and Hochschild Homology. Funct. anal. appl. 19 (1985), 4, 82-83. 
  8. [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. Zbl0748.58008
  9. [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. [10] Y. Nambu, Generalized Hamiltonian Dynamics. Phys. Review D7 (1973), 8, 2405-2412. Zbl1027.70503
  11. [11] L. Takhtajan, On Foundation of the Generalized Nambu Mechanics. Commun. Math. Phys. 160 (1994), 295-315. Zbl0808.70015
  12. [12] L. Takhtajan, Higher Order Analog of Chevalley-Eilenberg Complex and Deformation theory of N -gebras. Algebra and Analysis, 6 (1994), 2, 262-272. Zbl0833.17021
  13. [13] Yu. L. Daletskii, Hamiltonian Operators in Graded Formal Calculus of Variations. Funct. anal. appl. 20 (1986), 2, 62-64. 
  14. [14] B. A. Kupershmidt, Elements of Superintegrable Systems. Reidel, 1987. Zbl0621.58003
  15. [15] A. Connes, Géométrie Non Commutative. InterEditions, 1990. 
  16. [16] S. L. Woronowicz, Differential Calculus on Compact Matrix Pseudogroups (Quantum Groups). Commun. Math. Phys. 122 (1989), 125-170. Zbl0751.58042

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