Geodesic
Cohomologies of the Lie Algebra of Vector Fields on a Line
Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 2, pp. 147-160 
V. V. Zharinov. Cohomologies of the Lie Algebra of Vector Fields on a Line. Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 2, pp. 147-160. http://geodesic.mathdoc.fr/item/TMF_2001_128_2_a0/
@article{TMF_2001_128_2_a0,
     author = {V. V. Zharinov},
     title = {Cohomologies of the {Lie} {Algebra} of {Vector} {Fields} on a {Line}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {147--160},
     year = {2001},
     volume = {128},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_128_2_a0/}
}
TY  - JOUR
AU  - V. V. Zharinov
TI  - Cohomologies of the Lie Algebra of Vector Fields on a Line
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2001
SP  - 147
EP  - 160
VL  - 128
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2001_128_2_a0/
LA  - ru
ID  - TMF_2001_128_2_a0
ER  - 
%0 Journal Article
%A V. V. Zharinov
%T Cohomologies of the Lie Algebra of Vector Fields on a Line
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2001
%P 147-160
%V 128
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2001_128_2_a0/
%G ru
%F TMF_2001_128_2_a0

Voir la notice de l'article provenant de la source Math-Net.Ru

Providing adequate mathematical tools, we find cohomologies of the Lie algebra of smooth vector fields on a line with coefficients in the trivial, natural, and adjoint representations. We construct the generalized series of complexes and calculate the corresponding cohomologies.

[1] P. Karte, “Kogomologii algebr Li”, Teoriya algebr Li. Topologiya grupp Li, Seminar “Sofus Li”, IL, M., 1962, 32

[2] D. B. Fuks, Kogomologii beskonechnomernykh algebr Li, Nauka, M., 1984 | MR | Zbl

[3] B. L. Feigin, D. B. Fuks, “Kogomologii grupp i algebr Li”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 21, VINITI, M., 1988, 121 | MR

[4] J. A. de Azcárraga, J. M. Izquierdo, J. C. Pérez Bueno, An introduction to some novel applications of Lie algebra cohomology in mathematics and physics, E-print physics/9803046 | MR

[5] I. M. Gelfand, D. B. Fuks, Funkts. analiz i ego prilozh., 2:4 (1968), 92 | MR | Zbl

[6] L. Khermander, Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi. T. 1. Teoriya raspredelenii i analiz Fure, Mir, M., 1986 | MR

[7] T. Tsujishita, Proc. Japan Acad. A, 53 (1977), 134 | DOI | MR | Zbl

[8] M. V. Losik, Funkts. analiz i ego prilozh., 6:4 (1972), 44 | MR | Zbl

[9] V. N. Reshetnikov, DAN SSSR, 208:5 (1973), 1041 | Zbl