Geodesic
Cohomology of skew-holomorphic Lie algebroids
Teoretičeskaâ i matematičeskaâ fizika, Tome 165 (2010) no. 3, pp. 426-439 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We introduce the notion of a skew-holomorphic Lie algebroid on a complex manifold and explore some cohomology theories that can be associated with it. We present examples and applications of this notion in terms of different types of holomorphic Poisson structures.
Keywords: holomorphic Lie algebroid, matching pair of Lie algebroids, Lie algebroid cohomology, holomorphic Poisson cohomology. 
@article{TMF_2010_165_3_a2,
     author = {U. Bruzzo and V. N. Rubtsov},
     title = {Cohomology of skew-holomorphic {Lie} algebroids},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {426--439},
     year = {2010},
     volume = {165},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_165_3_a2/}
}
TY  - JOUR
AU  - U. Bruzzo
AU  - V. N. Rubtsov
TI  - Cohomology of skew-holomorphic Lie algebroids
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2010
SP  - 426
EP  - 439
VL  - 165
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2010_165_3_a2/
LA  - ru
ID  - TMF_2010_165_3_a2
ER  - 
%0 Journal Article
%A U. Bruzzo
%A V. N. Rubtsov
%T Cohomology of skew-holomorphic Lie algebroids
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2010
%P 426-439
%V 165
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2010_165_3_a2/
%G ru
%F TMF_2010_165_3_a2
U. Bruzzo; V. N. Rubtsov. Cohomology of skew-holomorphic Lie algebroids. Teoretičeskaâ i matematičeskaâ fizika, Tome 165 (2010) no. 3, pp. 426-439. http://geodesic.mathdoc.fr/item/TMF_2010_165_3_a2/

[1] C. Laurent-Gengoux, M. Stiénon, P. Xu, Int. Math. Res. Not., 2008 (2008), Art. ID rnn 088, 46 pp., arXiv: 0707.4253 | MR | Zbl

[2] S. Evens, J. -H. Lu, A. Weinstein, Quart. J. Math. Oxford Ser. (2), 50:200 (1999), 417–436 | DOI | MR | Zbl

[3] L. A. Cordero, M. Fernández, R. Ibáñez, L. Ugarte, Ann. Global Anal. Geom., 18:3–4 (2000), 265–290 | DOI | MR | Zbl

[4] V. V. Lychagin, V. N. Rubtsov, “Non-holonomic filtration: algebraic and geometric aspects of non-integrability”, Geometry in Partial Differential Equations, eds. A. Prastaro, Th. M. Rassias, World Sci., River Edge, NJ, 1994, 189–214 | DOI | MR | Zbl

[5] C. Voisin, Hodge Theory and Complex Algebraic Geometry, v. I, Cambridge Stud. Adv. Math., 76, Cambridge Univ. Press, Cambridge, 2007 | MR | Zbl

[6] I. Vaisman, Cohomology and Differential Forms, Pure Appl. Math., 21, Marcel Dekker, New York, 1973 | MR | Zbl

[7] V. N. Rubtsov, UMN, 35:4(214) (1980), 209–210 | DOI | MR | Zbl

[8] K. C. H. Mackenzie, General Theory of Lie Groupoids and Lie Algebroids, London Math. Soc. Lecture Note Ser., 213, Cambridge Univ. Press, Cambridge, 2005 | MR | Zbl

[9] J.-H. Lu, Duke Math. J., 86:2 (1997), 261–304 | DOI | MR | Zbl

[10] K. C. H. Mackenzie, Electron. Res. Announc. Amer. Math. Soc., 4 (1998), 74–87 | DOI | MR | Zbl

[11] T. Mokri, Glasgow Math. J., 39:2 (1997), 167–181 | DOI | MR | Zbl

[12] J. Huebschmann, “Differential Batalin–Vilkovisky algebras arising from twilled Lie–Rinehart algebras”, Poisson Geometry, Banach Center Publ., 51, eds. J. Grabowski, P. Urbański, Polish Acad. Sci., Warsaw, 2000, 87–102 | MR | Zbl

[13] U. Bruzzo, V. Rubtsov, On compatibility of Lie algebroid structures, in preparation

[14] J. F. Cariñena, J. M. Nuñes da Costa, P. Santos, J. Phys. A, 39:22 (2006), 6897–6918 | DOI | MR | Zbl