Geodesic
On the algebraic structure of the Lie algebra of vector fields on the line
Sbornik. Mathematics, Tome 62 (1989) no. 1, pp. 83-94 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The author obtains a description of the structure of a representation of the symmetric group $S_n$ in the space of $n$-linear elements of the variety of Lie algebras generated by the Lie algebra of vector fields on the line. It is proved that this space, as an $S_n$-module, is isomorphic to the space of homogeneous harmonic polynomials of degree $n-1$ in $n$ variables. Bibliography: 16 titles. 
@article{SM_1989_62_1_a4,
     author = {A. I. Molev},
     title = {On the algebraic structure of the {Lie} algebra of vector fields on the line},
     journal = {Sbornik. Mathematics},
     pages = {83--94},
     year = {1989},
     volume = {62},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_62_1_a4/}
}
TY  - JOUR
AU  - A. I. Molev
TI  - On the algebraic structure of the Lie algebra of vector fields on the line
JO  - Sbornik. Mathematics
PY  - 1989
SP  - 83
EP  - 94
VL  - 62
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1989_62_1_a4/
LA  - en
ID  - SM_1989_62_1_a4
ER  - 
%0 Journal Article
%A A. I. Molev
%T On the algebraic structure of the Lie algebra of vector fields on the line
%J Sbornik. Mathematics
%D 1989
%P 83-94
%V 62
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1989_62_1_a4/
%G en
%F SM_1989_62_1_a4
A. I. Molev. On the algebraic structure of the Lie algebra of vector fields on the line. Sbornik. Mathematics, Tome 62 (1989) no. 1, pp. 83-94. http://geodesic.mathdoc.fr/item/SM_1989_62_1_a4/

[1] Sumenkov E. A., “Odin primer v teorii algebr Li”, Tretii Vsesoyuzn. simpozium po teorii kolets, algebr i modulei. Tezisy soobschenii, Tartu, 1976, 97–98

[2] Bergman G., The Lie algebras of vector fields in $\mathbf{R}^n$ satisfies polinomial identities, Preprint, Berkeley, California, 1978, P. 1–27 | Zbl

[3] Razmyslov Yu. P., “Prostye algebry Li, udovletvoryayuschie standartnomu lievu tozhdestvu stepeni 5”, Izv. AN SSSR. Ser. matem., 49:3 (1985), 592–634 | MR | Zbl

[4] Kirillov A. A., Kontsevich M. L., “Rost algebry Li, porozhdennoi dvumya obschimi vektornymi polyami na pryamoi”, Vestn. MGU. Ser. 1. Matem., mekh., 1984, no. 4, 15–20 | MR

[5] Molev A. I., “Dokazatelstvo formuly Kirillova–Kontsevicha”, UMN, 39:1 (1984), 145–146 | MR | Zbl

[6] Kirillov A. A., Kontsevich M. L., Molev A. I., Algebry promezhutochnogo rosta., Preprint IPM im. M. V. Keldysha AN SSSR No 39, 1983 | MR

[7] Kirillov A. A., Molev A. I., Ob algebraicheskoi strukture algebry Li vektornykh polei, Preprint IPM im. M. V. Keldysha AN SSSR No 168, 1985 | MR

[8] Molev A. I., “O roste nekotorykh algebr Li vektornykh polei”, UMN, 41:2 (1986), 205–206 | MR | Zbl

[9] Kirillov A. A., Ovsienko V. Yu., Udalova O. D., O tozhdestvakh v algebre Li vektornykh polei na pryamoi, Preprint IPM im. M. V. Keldysha AN SSSR No 135, 1984 | MR

[10] Bakhturin Yu. A., Tozhdestva v algebrakh Li, Nauka, M., 1985 | MR | Zbl

[11] Kirillov A. A., O tozhdestvakh algebry Li gamiltonovykh vektornykh polei na ploskosti, Preprint IPM im. M. V. Keldysha AN SSSR No 121, 1983 | MR

[12] Molev A. I., Tsalenko L. M., “Predstavlenie simmetricheskoi gruppy v svobodnoi (super)algebre Li i v prostranstve garmonicheskikh mnogochlenov”, Funktsion. analiz i ego pril., 20:2 (1986), 76–77 | MR | Zbl

[13] Endryus G., Teoriya razbienii, Nauka, M., 1982 | MR

[14] Dzheims G., Teoriya predstavlenii simmetricheskikh grupp, Mir, M., 1982 | MR

[15] Makdonal'd I. G., Simmetricheskie funktsii i mnogochleny Kholla, Mir, M., 1985 | MR

[16] Mamford D., Algebraicheskaya geometriya. Kompleksnye proektivnye mnogoobraziya, Mir, M., 1979 | MR