This is a preview of subscription content, log in via an institution to check access.
REFERENCES
D. Alekseevskii, P. W. Michor, and W. Ruppert, “Extensions of Lie algebras,” math. DG/0005042.
M. F. Atiyah, “Complex analytic connections in fibre bundles,” Trans. Amer. Math. Soc., 85, 181–207 (1957).
A. A. Beilinson and V. V. Schechtman, “Determinant bundles and Virasoro algebras,” Commun. Math. Phys., 118 No.4, 651–701 (1988).
J.-L. Brylinski, Loop Spaces, Characteristic Classes and Geometric Quantization, Progress in Math., Vol. 107 Birkhauser (1993).
J.-L. Brylinski, “Gerbes on complex reductive Lie groups,” math. DG/0002158.
A. Cannas da Silva and A. Weinstein, Geometric Models for Noncommutative Algebras, Berkeley Math. Lecture Notes, 10. Amer. Math. Soc., Providence, RI; Berkeley Center for Pure and Applied Mathematics, Berkeley, CA (1999), xiv+184 pp. ISBN: 0-8218-0952-0 (available at A. Weinstein homepage http://www.math.berkeley.edu/alanw/).
J. Giraud, Cohomologie non Abelienne, Grundlehren, 179 Springer-Verlag (1971).
A. Alan Carey, A. Mickelsson, and M. Murray, “Bundle gerbes applied to quantum field theory,” hep-th/9711133.
E. R. Sharpe, “Discrete torsion and gerbes, I, II,” hep-th/9909108, hep-th/9909120.
A. Cattaneo and G. Felder, “Poisson sigma models and symplectic groupoids,” math.SG/0003023.
M. Crainic and R. Fernandes, “Integrability of Lie brackets,” math.DG/0105033.
T. J. Courant, “Dirac manifolds,” Trans. Amer. Math. Soc., 319 631–661 (1990).
I. Dorfman, “Deformations of Hamiltonian structures and integrable systems,” In: Nonlinear and Turbulent Processes in Physics [in Russian], Vol. 3 (Kiev 1983), Harwood Academic Publ., Chur (1984), pp. 1313–1318.
M. V. Karasev, “Analogs of objects of the theory of Lie groups for nonlinear Poisson brackets,” Izv. Akad. Nauk SSSR, Ser. Mat., 50 No.3, 508–538, 638 (1986).
J.-L. Koszul, “Crochet de Schouten-Nijenhuis et cohomologie,” In: The Mathematical Heritage of Cartan (Lyon, 1984), Asterisque, Numero Hors Serie (1985), pp. 257–271.
S. Evens, J.-H. Lu, and A. Weinstein, “Transverse measures, the modular class, and a cohomology pairing for Lie algebroids,” Quart. J. Math. Oxford Ser. (2), 50 No.200, 417–436 (1999).
N. Hitchin, “Lectures on special Lagrangian submanifolds,” math. DG/9907034.
M. Kapranov, “Rozansky-Witten invariants via Atiyah classes,” alg-geom/9704009.
C. Klimcik and T. Strobl, “WZW-Poisson manifolds,” math.SG/0104189.
A. Levin and M. Olshanetsky, “Hamiltonian algebroid symmetries in W-gravity and Poisson sigma-model, ” hep-th/0010043.
Z.-J. Liu, A. Weinstein, and P. Xu, “Manin triples for Lie bialgebroids,” J. Diff. Geom., 45 547–57 (1997).
Z.-J. Liu and P. Xu, “Dirac structures and dynamical r-matrices”, math.DG/9903119
J. L. Loday, “Une version non commutative des algebres de Lie: les algebres de Leibniz,” Enseign. Math., 39 269–293 (1993).
K. Mackenzie, Lie Groupoids and Lie Algebroids in Differential Geometry, LMS Lecture Notes Series, Cambridge Univ. Press (1987). (See also K. Mackenzie’s homepage http://www.shef.ac.uk/pm1kch m/rwork.html for a bibliography list on algebroids and some comments on the history.)
F. Malikov, V. Schechtman, and A. Vaintrob, “Chiral de Rham complex,” math.AG/9803041.
F. Malikov and V. Schechtman, “Chiral de Rham complex. II,” math.AG/9901065.
D. Roytenberg, “Courant algebroids, derived brackets and even symplectic supermanifolds,” Ph.D. Thesis, University of California, Berkeley (1999), preprint math.DG/9910078.
D. Roytenberg and A. Weinstein, “Courant algebroids and strongly homotopy Lie algebras,” Lett. Math. Phys., 46, 81–93 (1998).
V. N. Rubtsov, “Cohomology of the Der-complex,” Uspekhi Mat. Nauk, 35 No.4(214), 209–210 (1980).
V. N. Rubtsov, “Relatively invariant Der-cohomology of modules,” Uspekhi Mat. Nauk, 38 No.1(229), 189–190 (1983).
P. Severa and A. Weinstein, “Poisson geometry with a 3-form background,” math.SG/0107133.
P. Bressler, Vertex Algebroid I, math. AG/0202185.
Additional information
__________
Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 117, Geometry, 2004.
Rights and permissions
About this article
Cite this article
Bressler, P., Chervov, A. Courant Algebroids. J Math Sci 128, 3030–3053 (2005). https://doi.org/10.1007/s10958-005-0251-7
Issue Date:
DOI: https://doi.org/10.1007/s10958-005-0251-7