Duality for Lie-Rinehart algebras and the modular class

Journal fur die Reine und Angewandte Mathematik

Volumn 510, Issue , 1999, Pages 103-159

  Huebschmann, Johannes ^a  

^a UNIV LILLE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033414931     PISSN: 00754102     EISSN: None     Source Type: Journal    
DOI: 10.1515/crll.1999.043     Document Type: Article

References (25)

1. R. Almeida and P. Molino, Suites d'Atiyah et feuilletages transversalement complètes, C. R. Acad. Sci. Paris I 300 (1985), 13-15.
2. R. Bieri, Homological dimension of discrete groups, Queen Mary College, Department of Pure Mathematics, London, U. K., 1976; 2nd edition: 1981, MR 57#6224, 84h:20047.
3. R. Bieri and B. Eckmann, Groups with homological duality generalizing Poincaré duality, Invent. Math. 20 (1973), 103-124.
4. A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces. I, Amer. J. Math. 80 (1958), 458-538; II, Amer. J. Math. 81 (1959), 315-382; III, Amer. J. Math. 82 (1960), 491-504.
5. A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces. I, Amer. J. Math. 80 (1958), 458-538; II, Amer. J. Math. 81 (1959), 315-382; III, Amer. J. Math. 82 (1960), 491-504.
6. A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces. I, Amer. J. Math. 80 (1958), 458-538; II, Amer. J. Math. 81 (1959), 315-382; III, Amer. J. Math. 82 (1960), 491-504.
7. A. Borel et al., D-modules, Perspect. Math. 2, J. Coates and S. Helgason, eds., Academic Press, Boston-Orlando-San Diego-New York-Austin-London-Sydney-Tokyo-Toronto 1987.
8. K.S. Brown, Homological criteria for finiteness, Comment. Math. Helv. 50 (1975), 129-135.
9. H. Cartan and S. Eilenberg, Homological Algebra, Princeton University Press, Princeton 1956.
10. S. Chemla, Poincaré duality for k-A Lie superalgebras, Bull. Soc. math. France 122 (1994), 371-397.
11. G. de Rham, Variétés diffërentiables, Hermann, Paris 1955.
12. S. Evens, J.-H. Lu, and A. Weinstein, Transverse measures, the modular class, and a cohomology pairing for Lie algebroids, Quart. J. Math., to appear.
13. V.L. Gin-burg and A. Weinstein, Lie-Poisson structure on some Poisson Lie groups, J. Amer. Math. Soc. 5 (1992), 445-453.
14. R. Godement, Topologie algébrique et théorie des faisceaux, Hermann, Paris 1964.
15. V.K.A.M. Gugenheim, On the chain complex of a fibration, Ill. J. Math. 16 (1972), 398-414.
16. R. Hartshorne, Algebraic Geometry, Grad. Texts Math. 52, Springer, Berlin-Göttingen-Heidelberg 1977.
17. J. Huebschmann, Poisson cohomology and quantization, J. reine angew. Math. 408 (1990), 57-113.
18. J. Huebschmann, Lie-Rinehart algebras, Gerstenhaber algebras, and Batalin-Vilkovisky algebras, Ann. Inst. Fourier 48 (1998), 425-440.
19. J. Huebschmann, Extensions of Lie-Rinehart algebras and the Chern-Weil construction, in: Festschrift in honor of J. Stasheff's 60th birthday, Cont. Math. 227 (1999), 145-176.
20. J.L. Koszul, Crochet de Schouten-Nijenhuis et cohomologie, in: E. Cartan et les Mathématiciens d'aujourd'hui, Lyon, 25-29 Juin, 1984, Astérisque hors-série (1985), 251-271.
21. K. Mackenzie, Lie groupoids and Lie algebroids in differential geometry, London Math. Soc. Lect. Note Ser. 124, Cambridge University Press, Cambridge, England 1987.
22. S. Mac Lane, Homology, Grundl. math. Wiss. 114, Springer, Berlin-Göttingen-Heidelberg 1963.
23. G. Rinehart, Differential forms for general commutative algebras, Trans. Amer. Math. Soc. 108 (1963), 195-222.
24. A. Weinstein, The modular automorphism group of a Poisson manifold, in: Special volume in honor of A. Lichnerowicz, J. Geom. Phys. 23 (1997), 379-394.
25. P. Xu, Gerstenhaber algebras and BV-algebras in Poisson geometry. Comm. math. phys., to appear.