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Generating Operators of the Krasil'shchik–Schouten Bracket

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Abstract

It is proved that given a divergence operator on the structural sheaf of graded commutative algebras of a supermanifold, it is possible to construct a generating operator for the Krashil'shchik–Schouten bracket. This is a particular case of the construction of generating operators for a special class of bigraded Gerstenhaber algebras. Also, some comments on the generalization of these results to the context of n-graded Jacobi algebras are included.

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References

  1. Batalin, I. A., and Vilkovisky, G. A.: Gauge algebra and quantization, Phys. Lett. B. 102(1) (1981), 27–31.

    Google Scholar 

  2. Grabowski, J., and Marmo, G.: The graded Jacobi algebras and (co)homology, J. Phys. A: Math. Gen. 36 (2003), pp. 161–181.

    Google Scholar 

  3. Kostant, B.: Graded manifolds, graded Lie theory, and prequantization, In: Differential Geometrical Methods in Math. Phys. (Proc. Sympos. Univ. Bonn, 1975), Lecture Notes in Math. 570, Springer, Berlin, 1977, pp. 177–306.

    Google Scholar 

  4. Kosmann-Schwarzbach, Y: Exact Gerstenhaber algebras and Lie bialgebroids, Acta Appl. Math. 41 (1995), 153–165.

    Google Scholar 

  5. Kosmann-Schwarzbach, Y: Graded Poisson brackets and field theory, In: J. Bertrand et al. (eds), Modern Group Theoretical Methods in Physics, Kluwer, Dordrecht, 1995, pp. 189–196.

    Google Scholar 

  6. Kosmann-Schwarzbach,Y., and Monterde, J: Divergence operators and odd Poisson brackets, Ann. Inst. Fourier 52 (2) (2002), 419–456.

    Google Scholar 

  7. Koszul, J. L: Crochet de Schouten–Nijenhuis et cohomologie, Astérisque, Hors série 1985, pp. 257–271.

  8. Krasil'shchick, I. S.: Supercanonical algebras and Schouten brackets, Mat Zametki 49 (1) (1991), 70–76; Math. Notes 49 (1) (1991), 50–54.

    Google Scholar 

  9. Leites, D. A: Introduction to the theory of supermanifolds, Russian Math. Surveys 35 (1980), 1–64.

    Google Scholar 

  10. Michor, P. W: Remarks on the Schouten–Nijenhuis bracket, Proc. Winter School on Geometry and Physics (Srní, 1987), Rend. Circ. Mat. Palermo 2 (Suppl. 16) (1987), 207–215.

    Google Scholar 

  11. Schwarz, A. S: geometry of Batalin–Vilkovisky quantization, Comm. Math. Phys. 155 (1993), 249–260.

    Google Scholar 

  12. Serre, J. P: Un théorè me de dualité, Comment Math. Helv. 29 (1955), 9–26.

    Google Scholar 

  13. Witten, E. A note on the antibracket formalism, Modern Phys. Lett. A 5 (1990), 487–494.

    Google Scholar 

  14. Wu, J., Gerstenhaber, M., and Stasheff, J.: On the Hodge decomposition of differential graded bialgebras, J. Pure Appl. Algebra 162 (1) (2001), 103–125.

    Google Scholar 

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  1. Dept. Geometria i Topologia Universitat de València Av, Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, Lat., V. A. Estellés 1, Av, Salvador Nava s/n, Spain México)

    José Vallejo

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Vallejo, J. Generating Operators of the Krasil'shchik–Schouten Bracket. Letters in Mathematical Physics 68, 1–17 (2004). https://doi.org/10.1007/s11005-004-4066-0

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