Keywords: BRST differential, integrable system, string theory.
@article{TMF_2011_167_3_a8,
author = {A. V. Kiselev and J. W. van de Leur},
title = {Variational {Lie} algebroids and homological evolutionary vector},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {432--447},
year = {2011},
volume = {167},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a8/}
}
A. V. Kiselev; J. W. van de Leur. Variational Lie algebroids and homological evolutionary vector. Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 3, pp. 432-447. http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a8/
[1] A. Yu. Vaintrob, UMN, 52:2(314) (1997), 161–162 | DOI | MR | Zbl
[2] M. Alexandrov, A. Schwarz, O. Zaboronsky, M. Kontsevich, Internat. J. Modern Phys. A, 12:7 (1997), 1405–1429, arXiv: hep-th/9502010 | DOI | MR | Zbl
[3] Y. Kosmann-Schwarzbach, SIGMA, 4 (2008), 005, 30 pp., arXiv: ; Lett. Math. Phys., 69:1–3 (2004), 61–87, arXiv: ; Ann. Inst. Fourier (Grenoble), 46:5 (1996), 1243–1274 0710.3098math/0312524 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl
[4] A. V. Bocharov, A. M. Verbovetskii, A. M. Vinogradov, S. V. Duzhin, I. S. Krasilschik, A. V. Samokhin, Yu. N. Torkhov, N. G. Khorkova, V. N. Chetverikov, Simmetrii i zakony sokhraneniya uravnenii matematicheskoi fiziki, Faktorial, M., 2005 | MR | Zbl
[5] T. Voronov, “Graded manifolds and Drinfeld doubles for Lie bialgebroids”, Quantization, Poisson Brackets and Beyond, Contemp. Math., 315, ed. T. Voronov, AMS, Providence, RI, 2002, 131–168 | DOI | MR | Zbl
[6] J.-C. Herz, C. R. Acad. Sci. Paris, 263 (1953), 1935–1937 ; 2289–2291 | MR | MR | Zbl
[7] Y. Kosmann-Schwarzbach, F. Magri, Ann. Inst. H. Poincaré, 53:1 (1990), 35–81 | MR | Zbl
[8] A. V. Kiselev, I. V. van de Ler, TMF, 162:2 (2010), 179–195, arXiv: 0902.3624 | DOI | MR | Zbl
[9] A. N. Leznov, M. V. Saveliev, Lett. Math. Phys., 3:6 (1979), 489–494 | DOI | MR | Zbl
[10] A. V. Zhiber, V. V. Sokolov, UMH, 56:1(337) (2001), 63–106 | DOI | MR | Zbl
[11] A. Kumpera, D. C. Spencer, Lie Equations, v. I, Ann. Math. Stud., 73, General theory, Princeton Univ. Press, Princeton, N.J.; Univ. Tokyo Press, Tokyo, 1972 | MR | Zbl
[12] J. Krasil'shchik, A. Verbovetsky, “Geometry of jet spaces and integrable systems”, J. Geom. Phys. (to appear) , arXiv: 1002.0077 | DOI | MR
[13] B. A. Kupershmidt, “Geometry of jet bundles and the structure of Lagrangian and Hamiltonian formalisms”, Geometric Methods in Mathematical Physics, Lecture Notes in Math., 775, Springer, Berlin, 1980, 162–218 | DOI | MR | Zbl
[14] P. Olver, Prilozheniya grupp Li k differentsialnym uravneniyam, Mir, M., 1989 | MR | MR | Zbl
[15] A. V. Kiselev, TMF, 144:1 (2005), 83–93, arXiv: nlin.SI/0409061 | DOI | MR | Zbl
[16] A. V. Kiselev, J. W. van de Leur, J. Phys. A, 42:40 (2009), 404011, 8 pp., arXiv: 0903.1214 | DOI | MR | Zbl
[17] A. V. Kiselev, J. W. van de Leur, Involutive distributions of operator-valued evolutionary vector fields and their affine geometry, Preprint IHES/M/07/38, Inst. Hautes Études Sci., Bures-sur-Yvette | MR
[18] P. Kersten, I. Krasil'shchik, A. Verbovetsky, J. Geom. Phys., 50:1–4 (2004), 273–302, arXiv: math/0304245 | DOI | MR | Zbl
[19] M. Nesterenko, R. Popovych, J. Math. Phys., 47:12 (2006), 123515, 45 pp., arXiv: math-ph/0608018 | DOI | MR | Zbl
[20] C. P. Boyer, J. D. Finley III, J. Math. Phys., 23:6 (1982), 1126–1130 | DOI | MR | Zbl
[21] V. A. Golovko, I. S. Krasilschik, A. M. Verbovetskii, TMF, 154:2 (2008), 268–282, arXiv: 0812.4684 | DOI | MR | Zbl
[22] T. Lada, J. Stasheff, Internat. J. Theoret. Phys., 32:7 (1993), 1087–1103, arXiv: hep-th/9209099 | DOI | MR | Zbl
[23] A. V. Kiselev, Fundament. i prikl. matem., 11:1 (2005), 159–180, arXiv: math.RA/0410185 | DOI | MR | Zbl
[24] P. Kersten, I. Krasil'shchik, A. Verbovetsky, Acta Appl. Math., 83:1–2 (2004), 167–173, arXiv: math/0310451 | DOI | MR | Zbl
[25] P. A. M. Dirak, Lektsii po kvantovoi mekhanike, Mir, M., 1968 ; T. de Donder, Théorie invariantive du calcul des variations, Gauthier-Villars, Paris, 1930 | MR | Zbl | Zbl
[26] I. S. Krasilschik, A. M. Verbovetskii, Gomologicheskie metody v teorii uravnenii matematicheskoi fiziki, 1999, arXiv: math.DG/9808130