Identities on solutions of the wave equation in the enveloping algebra of the conformal group
Teoretičeskaâ i matematičeskaâ fizika, Tome 83 (1990) no. 1, pp. 14-22 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The enveloping algebra of the conformal-group algebra of Minkowski space is regarded as an algebra of differential symmetry operators of the wave equation. It is shown that this algebra is graded. The structure of the enveloping algebra and of its ideal is investigated by means of the grading. The ideal consists of identities of elements of the enveloping algebra on solutions of the wave equation. All identities that consist of second-order operators are found.
@article{TMF_1990_83_1_a1,
     author = {V. G. Bagrov and B. F. Samsonov and A. V. Shapovalov and I. V. Shirokov},
     title = {Identities on~solutions of~the wave equation in~the enveloping algebra of~the conformal group},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {14--22},
     year = {1990},
     volume = {83},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1990_83_1_a1/}
}
TY  - JOUR
AU  - V. G. Bagrov
AU  - B. F. Samsonov
AU  - A. V. Shapovalov
AU  - I. V. Shirokov
TI  - Identities on solutions of the wave equation in the enveloping algebra of the conformal group
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1990
SP  - 14
EP  - 22
VL  - 83
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1990_83_1_a1/
LA  - ru
ID  - TMF_1990_83_1_a1
ER  - 
%0 Journal Article
%A V. G. Bagrov
%A B. F. Samsonov
%A A. V. Shapovalov
%A I. V. Shirokov
%T Identities on solutions of the wave equation in the enveloping algebra of the conformal group
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1990
%P 14-22
%V 83
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1990_83_1_a1/
%G ru
%F TMF_1990_83_1_a1
V. G. Bagrov; B. F. Samsonov; A. V. Shapovalov; I. V. Shirokov. Identities on solutions of the wave equation in the enveloping algebra of the conformal group. Teoretičeskaâ i matematičeskaâ fizika, Tome 83 (1990) no. 1, pp. 14-22. http://geodesic.mathdoc.fr/item/TMF_1990_83_1_a1/

[1] Bateman H., Proc. Lond. Math. Soc., 8 (1910), 223 | DOI | Zbl

[2] Ibragimov N. Kh., Gruppovye svoistva nekotorykh differentsialnykh uravnenii, Nauka, Novosibirsk, 1967 | MR

[3] Ibragimov N. Kh., DAN SSSR, 178:3 (1968), 566–568 | MR

[4] Ovsyannikov L. V., Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR

[5] Fuschich V. I., Nikitin A. G., Simmetriya uravnenii Maksvella, Naukova dumka, Kiev, 1983 | MR

[6] Shapovalov V. N., Izv. vuzov. Fizika, 1977, no. 6, 57–64; 64–70

[7] Kalnins E. G., Miller W. Jr., J. Math. Phys., 18:1 (1977), 1–16 | DOI | MR | Zbl

[8] Kalnins E. G., Miller W. Jr., SIAM. J. Math. Anal., 9:1 (1978), 12–33 | DOI | MR | Zbl

[9] Kalnins E. G., Miller W. Jr., J. Math. Phys., 18:12 (1977), 271–280 | DOI | MR | Zbl

[10] Kalnins E. G., Miller W. Jr., J. Math. Phys., 19:6 (1978), 1233–1246 | DOI | MR | Zbl

[11] Kalnins E. G., Miller W. Jr., J. Math. Phys., 19:6 (1978), 1247–1257 | DOI | MR | Zbl

[12] Kotelnikov G. A., Teoretiko-gruppovye metody v fizike, Nauka, M., 1983, 431–439

[13] Shapovalov V. N., Diff. uravneniya, 16:10 (1980), 1864–1874 | MR | Zbl

[14] Bagrov V. G., Samsonov B. F., Shapovalov A. V., Shirokov I. V., Kommutativnye podalgebry operatorov simmetrii pervogo poryadka volnovogo uravneniya, Preprint No 31, TF SO AN SSSR, Tomsk, 1988

[15] Bagrov V. G., Samsonov B. F., Shapovalov A. V., Shirokov I. V., Polnye nabory operatorov simmetrii pervogo poryadka i razdelenie peremennykh v volnovom uravnenii, Preprint No 38, TF SO AN SSSR, Tomsk, 1988

[16] Shapovalov A. V., Shirokov I. V., Sovremennyi gruppovoi analiz, Preprint, Leningradskii in-t informatiki AN SSSR, L., 1990

[17] Kirillov A. A., Elementy teorii predstavlenii, Nauka, M., 1978 | MR | Zbl