Geodesic
Homology of the Lie Algebra of Vector Fields on the Line with Coefficients in Symmetric Powers of its Adjoint Representation
Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 2, pp. 13-19.

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

We compute the homology of the Lie algebra $W_1$ of (polynomial) vector fields on the line with coefficients in symmetric powers of its adjoint representation. We also list the results obtained so far for the homology with coefficients in tensor powers and, in turn, use them for partially computing the homology of the Lie algebra of $W_1$-valued currents on the line. 
@article{FAA_2006_40_2_a1,
     author = {V. V. Dotsenko},
     title = {Homology of the {Lie} {Algebra} of {Vector} {Fields} on the {Line} with {Coefficients} in {Symmetric} {Powers} of its {Adjoint} {Representation}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {13--19},
     publisher = {mathdoc},
     volume = {40},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2006_40_2_a1/}
}
TY  - JOUR
AU  - V. V. Dotsenko
TI  - Homology of the Lie Algebra of Vector Fields on the Line with Coefficients in Symmetric Powers of its Adjoint Representation
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2006
SP  - 13
EP  - 19
VL  - 40
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2006_40_2_a1/
LA  - ru
ID  - FAA_2006_40_2_a1
ER  - 
%0 Journal Article
%A V. V. Dotsenko
%T Homology of the Lie Algebra of Vector Fields on the Line with Coefficients in Symmetric Powers of its Adjoint Representation
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2006
%P 13-19
%V 40
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2006_40_2_a1/
%G ru
%F FAA_2006_40_2_a1
V. V. Dotsenko. Homology of the Lie Algebra of Vector Fields on the Line with Coefficients in Symmetric Powers of its Adjoint Representation. Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 2, pp. 13-19. http://geodesic.mathdoc.fr/item/FAA_2006_40_2_a1/

[1] B. L. Feigin, B. L. Tsygan, “Riemann–Roch theorem and Lie algebra homology”, Proc. of the Winter School on Geometry and Physics (Srni, 9–16 January 1988), Rend. Circ. Mat. Palermo (2) Suppl., 21, 1989, 15–52 | MR | Zbl

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

[3] A. Kartan, S. Eilenberg, Gomologicheskaya algebra, IL, M., 1960