Symmetries of a flat cosymbol algebra of the differential operators
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 95-105 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In this paper the structure theorem is proved for graded symmetries of a flat cosymbol algebra. This theorem together with Equivariant Polynomials Lemma gives an upper bound on the grade dimensions of the Lie algebra of symmetries.
@article{ZNSL_2016_443_a8,
     author = {V. S. Kalnitsky},
     title = {Symmetries of a~flat cosymbol algebra of the differential operators},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {95--105},
     year = {2016},
     volume = {443},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a8/}
}
TY  - JOUR
AU  - V. S. Kalnitsky
TI  - Symmetries of a flat cosymbol algebra of the differential operators
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2016
SP  - 95
EP  - 105
VL  - 443
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a8/
LA  - ru
ID  - ZNSL_2016_443_a8
ER  - 
%0 Journal Article
%A V. S. Kalnitsky
%T Symmetries of a flat cosymbol algebra of the differential operators
%J Zapiski Nauchnykh Seminarov POMI
%D 2016
%P 95-105
%V 443
%U http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a8/
%G ru
%F ZNSL_2016_443_a8
V. S. Kalnitsky. Symmetries of a flat cosymbol algebra of the differential operators. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 95-105. http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a8/

[1] A. M. Vinogradov, “Geometriya nelineinykh differentsialnykh uravnenii”, Itogi nauki i tekhn. Ser. Probl. geom., 11, VINITI, M., 1980, 89–134 | MR | Zbl

[2] I. S. Krasil'shchik, “Calculus over Commutative Algebras: A Concise User Guide”, Acta Applicandae Mathematicae, 49 (1997), 235–248 | DOI | MR | Zbl

[3] G. Vezzosi, A. M. Vinogradov, “On higher order analogues of de Rham cohomology”, Differential Geom. Appl., 19:1 (2003), 29–59 | DOI | MR | Zbl

[4] I. S. Krasil'shchik, V. V. Lychagin, A. M. Vinogradov, Geometry of jet spaces and nonlinear partial differential equations, v. 1, Advanced Studies in Contemporary Mathematics, Gordon and Breach Science Publishers, New York, 1986 | MR | Zbl

[5] I. S. Krasil'shchik, B. Prinari, Lectures on Linear Differential Operators over Commutative Algebras, The Diffiety Inst. Preprint Series, DIPS 1/99

[6] A. M. Vinogradov, V. S. Kalnitskii, Printsip nablyudaemosti v primerakh i zadachakh, Izd. Dom SPbGU, 2012

[7] V. S. Kalnitskii, “Algebra obobschennykh polei Yakobi”, Zap. nauchn. semin. POMI, 231, 1995, 222–244 | MR | Zbl

[8] V. V. Kozlov, N. V. Denisova, “Polinomialnye integraly geodezicheskikh potokov na dvumernom tore”, Matem. sb., 185:12 (1994), 49–64 | MR | Zbl

[9] V. V. Kozlov, “O gruppakh simmetrii dinamicheskikh sistem”, PMM, 52:4 (1988), 531–541 | MR | Zbl

[10] V. V. Kozlov, “O gruppakh simmetrii geodezicheskikh potokov na zamknutykh poverkhnostyakh”, Matem. zametki, 48:5 (1990), 62–67 | MR | Zbl

[11] N. V. Denisova, V. V. Kozlov, “Polinomialnye integraly obratimykh mekhanicheskikh sistem s konfiguratsionnym prostranstvom v vide dvumernogo tora”, Matem. sb., 191:2 (2000), 43–63 | DOI | MR | Zbl

[12] A. M. Vinogradov, I. S. Krasilschik, “Chto takoe gamiltonov formalizm?”, UMN, 30:1(181) (1975), 173–198 | MR | Zbl

[13] Dzhet Nestruev, Gladkie mnogoobraziya i nablyudaemye, MTsNMO, M., 2000

[14] V. V. Kozlov, N. V. Denisova, “Simmetrii i topologiya dinamicheskikh sistem s dvumya stepenyami svobody”, Matem. sb., 184:9 (1993), 125–148 | MR | Zbl