Geodesic
Cohomology of Graded Lie Algebras of Maximal Class with Coefficients in the Adjoint Representation
Informatics and Automation, Geometry, topology, and mathematical physics. I, Tome 263 (2008), pp. 106-119.

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

We compute explicitly the adjoint cohomology of two $\mathbb N$-graded Lie algebras of maximal class (infinite-dimensional filiform Lie algebras) $\mathfrak m_0$ and $\mathfrak m_2$. It is known that up to an isomorphism there are only three $\mathbb N$-graded Lie algebras of maximal class. The third algebra from this list is the “positive” part $L_1$ of the Witt (or Virasoro) algebra, and its adjoint cohomology was computed earlier by Feigin and Fuchs. 
@article{TRSPY_2008_263_a7,
     author = {D. V. Millionshchikov},
     title = {Cohomology of {Graded} {Lie} {Algebras} of {Maximal} {Class} with {Coefficients} in the {Adjoint} {Representation}},
     journal = {Informatics and Automation},
     pages = {106--119},
     publisher = {mathdoc},
     volume = {263},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2008_263_a7/}
}
TY  - JOUR
AU  - D. V. Millionshchikov
TI  - Cohomology of Graded Lie Algebras of Maximal Class with Coefficients in the Adjoint Representation
JO  - Informatics and Automation
PY  - 2008
SP  - 106
EP  - 119
VL  - 263
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2008_263_a7/
LA  - ru
ID  - TRSPY_2008_263_a7
ER  - 
%0 Journal Article
%A D. V. Millionshchikov
%T Cohomology of Graded Lie Algebras of Maximal Class with Coefficients in the Adjoint Representation
%J Informatics and Automation
%D 2008
%P 106-119
%V 263
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2008_263_a7/
%G ru
%F TRSPY_2008_263_a7
D. V. Millionshchikov. Cohomology of Graded Lie Algebras of Maximal Class with Coefficients in the Adjoint Representation. Informatics and Automation, Geometry, topology, and mathematical physics. I, Tome 263 (2008), pp. 106-119. http://geodesic.mathdoc.fr/item/TRSPY_2008_263_a7/

[1] Goncharova L. V., “Kogomologii algebr Li formalnykh vektornykh polei na pryamoi”, Funkts. analiz i ego pril., 7:2 (1973), 6–14 | MR | Zbl

[2] Millionschikov D. V., “Nekotorye spektralnye posledovatelnosti v analiticheskoi teorii gomotopii”, Mat. zametki, 47:5 (1990), 52–61 | MR | Zbl

[3] Feigin B. L., Fuks D. B., “Gomologii algebry Li vektornykh polei na pryamoi”, Funkts. analiz i ego pril., 14:3 (1980), 45–60 | MR | Zbl

[4] Fialovski A., “Klassifikatsiya graduirovannykh algebr Li s dvumya obrazuyuschimi”, Vestn. Mosk. un-ta. Matematika. Mekhanika, 1983, no. 2, 62–64 | MR

[5] Goze M., Khakimdjanov Yu., Nilpotent Lie algebras, Math. and Appl., 361, Kluwer Acad. Publ., Dordrecht, 1996 | MR | Zbl

[6] Fialowski A., Millionschikov D., “Cohomology of graded Lie algebras of maximal class”, J. Algebra, 296:1 (2006), 157–176 | DOI | MR | Zbl

[7] Fialowski A., Wagemann F., “Cohomology and deformations of the infinite-dimensional filiform Lie algebra $\mathfrak m_0$”, J. Algebra, 318:2 (2007), 1002–1026 ; arxiv: math/0703383v2[math.RT] | DOI | MR | Zbl

[8] Fialowski A., Wagemann F., “Cohomology and deformations of the infinite-dimensional filiform Lie algebra $\mathfrak m_2$”, J. Algebra, 319:12 (2008), 5125–5143 ; arxiv: 0708.0363v2[math.RT] | DOI | MR | Zbl

[9] Hakimjanov You. B., “Variété des lois d'algèbres de Lie nilpotentes”, Geom. Dedicata, 40 (1991), 269–295 | DOI | MR | Zbl

[10] Shalev A., Zelmanov E. I., “Narrow Lie algebras: a coclass theory and a characterization of the Witt algebra”, J. Algebra, 189:2 (1997), 294–331 | DOI | MR | Zbl

[11] Vergne M., “Cohomologie des algèbres de Lie nilpotentes. Application à l'étude de la variété des algèbres de Lie nilpotentes”, Bull. Soc. Math. France, 98 (1970), 81–116 | MR | Zbl