Geodesic
Associative homotopy Lie algebras and Wronskians
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 1, pp. 159-180.

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We analyze representations of Schlessinger–Stasheff associative homotopy Lie algebras by higher-order differential operators. $W$-transformations of chiral embeddings of a complex curve related with the Toda equations into Kähler manifolds are shown to be endowed with the homotopy Lie-algebra structures. Extensions of the Wronskian determinants preserving Schlessinger–Stasheff algebras are constructed for the case of $n\geq1$ independent variables. 
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A. V. Kiselev. Associative homotopy Lie algebras and Wronskians. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 1, pp. 159-180. http://geodesic.mathdoc.fr/item/FPM_2005_11_1_a5/

[1] Bocharov A. V., Verbovetskii A. M., Vinogradov A. M. i dr., Simmetrii i zakony sokhraneniya uravnenii matematicheskoi fiziki, eds. A. M. Vinogradov, I. S. Krasilschik, Faktorial, M., 1997, 464 pp.

[2] Gelfand I. M., Fuks D. B., “Kogomologii algebry Li vektornykh polei na okruzhnosti”, Funktsion. analiz i ego pril., 2:4 (1968), 92–93 | MR

[3] Dzhumadildaev A. S., “O tselochislennykh i mod $p$-kogomologii algebry Li $W_1$”, Funktsion. analiz i ego pril., 22:3 (1988), 68–70 | MR

[4] Kasymov Sh. M., “Sopryazhënnost podalgebr Kartana v $n$-lievykh algebrakh”, Dokl. RAN, 345:1 (1995), 15–18 | MR | Zbl

[5] Kiselëv A. V., “O $(3,1,0)$-algebre Li gladkikh funktsii”, Trudy XXIII Konferentsii molodykh uchënykh (Mekhaniko-matematicheskii f-t MGU im. M. V. Lomonosova, Moskva, 9–14 aprelya 2001 g.), M., 2001, 157–158

[6] Kiselëv A. V., “Ob $n$-arnykh obobscheniyakh algebry Li $\mathfrak{sl}_2(\Bbbk)$”, Trudy XXIV Konferentsii molodykh uchënykh (Mekhaniko-matematicheskii f-t MGU im. M. V. Lomonosova, Moskva, 8–13 aprelya 2002 g.), M., 2002, 78–81

[7] Leznov A. N., Savelev M. V., Gruppovye metody integrirovaniya nelineinykh dinamicheskikh sistem, Nauka, M., 1985, 278 pp. | MR | Zbl

[8] Filippov V. T., “O lievykh $n$-algebrakh”, Sib. mat. zhurn., 24 (1985), 126–140 | MR

[9] De Azcárraga J. A., Perelomov A. M., Pérez Bueno J. C., “The Schouten–Nijenhuis bracket, cohomology, and generalized Poisson structure”, J. Phys. A: Math. Gen., 29 (1996), 7993–8009 | DOI | MR | Zbl

[10] Barnich G., Fulp R., Lada T., Stasheff J., “The sh Lie structure of Poisson brackets in field theory”, Comm. Math. Phys., 191 (1998), 585–601 | DOI | MR | Zbl

[11] Dzhumadil'daev A. S., Wronskians as $n$-Lie multiplications, arXiv: /math.RA/0202043 | MR

[12] Dzhumadil'daev A. S., $N$-commutators of vector fields, arXiv: /math.RA/0203036

[13] Gervais J.-L., Matsuo Y., “$W$-geometries”, Phys. Lett. B, 274 (1992), 309–316 | DOI | MR

[14] Gervais J.-L., Matsuo Y., “Classical $A_n$- $W$-geometries”, Comm. Math. Phys., 152 (1993), 317–368 | DOI | MR | Zbl

[15] Gervais J.-L., Saveliev M. V., “$W$-geometry of the Toda systems associated with non-exceptional Lie algebras”, Comm. Math. Phys., 180:2 (1996), 265–296 | DOI | MR | Zbl

[16] Hanlon P., Wachs M. L., “On Lie $k$-algebras”, Adv. in Math., 113 (1995), 206–236 | DOI | MR | Zbl

[17] Kassel Ch., Quantum Groups, Springer, 1995 | MR

[18] Kersten P., Krasil'shchik I., Verbovetsky A., Hamiltonian operators and $\ell^*$-coverings Diffiety Institute, Preprint DIPS-06/2002

[19] Lada T., Stasheff J. D., “Introduction to sh Lie algebras for physicists”, Int. J. Theor. Phys., 32 (1993), 1087–1103 | DOI | MR | Zbl

[20] Marvan M., Jet. A software for diferential calculus on jet spaces and diffieties, ver. 3.9 (August 1997) for Maple V Release 4, diffiety.ac.ru | MR

[21] Michor P., Vinogradov A. M., “$n$-ary Lie and associative algebras”, Rend. Sem. Mat. Univ. Pol. Torino, 53:4 (1996), 373–392 | MR

[22] Nambu Y., “Generalized Hamiltonian dynamics”, Phys. Rev. D, 7 (1973), 2405–2412 | DOI | MR | Zbl

[23] Sahoo D., Valsakumar M. C., “Nambu mechanics and its quantization”, Phys. Rev. A, 46 (1992), 4410–4412 | DOI

[24] Schlessinger M., Stasheff J. D., “The Lie algebra structure of tangent cohomology and deformation theory”, J. Pure Appl. Algebra, 38 (1985), 313–322 | DOI | MR | Zbl

[25] Takhtajan L., “On foundations of generalized Nambu mechanics”, Comm. Math. Phys., 160 (1994), 295–315 | DOI | MR | Zbl

[26] Vinogradov A., Vinogradov M., “On multiple generalizations of Lie algebras and Poisson manifolds”, Contemp. Math., 219 (1998), 273–287 | MR | Zbl