Articles by Yvette Kosmann-Schwarzbach

Courant algebroids, a short history, SIGMA
Dirac pairs, preprint, arXiv1104.1379.

Nijenhuis structures on Courant algebroids, Bull. Brazilian Math. Soc., 42  (4) (2011), 625-649,  arXiv1102.1410.

Poisson and symplectic functions in Lie algebroid theory, Higher Structures in Geometry and Physics, in honor of Murray Gerstenhaber and Jim Stasheff,
eds. Alberto Cattaneo, Antony Giaquinto and Ping Xu, Progress in Mathematics 287, Birkhauser, 2011, 243-268, arXiv:0711.2043

With Vladimir Rubtsov, Compatible structures on Lie algebroids and Monge-Ampère operators, Acta  Appl. Math., 109 (2010), no. 1, 101-135,

With Camille Laurent-Gengoux and Alan Weinstein, Modular classes of Lie algebroid morphisms, Transformation Groups, 13, no. 3-4 (2008), 27-755,
special issue in honor of Bertram Kostant, arXiv:0712.3021

Poisson manifolds, Lie algebroids, modular classes: a survey, SIGMA, 4 (2008), 005, 30 pages,, arXiv:0710.3098

Modular classes of Lie algebroids: recent results, Oberwolfach Reports,4 (2) 2007, 1270-1272.

With Milen Yakimov, Modular classes of regular twisted Poisson structures on Lie algebroids, Lett. Math. Phys., 80 (2007), 183-197, arXiv:math/0701209

(unpublished preprint) With Franco Magri, On the modular classes of Poisson-Nijenhuis manifolds, math.SG/0611202. 

With C. Laurent-Gengoux, The modular class of a twisted Poisson structure, Travaux Mathématiques (Luxembourg), 15 (2005), 315-339, math.SG/0505663.

With A. Weinstein, Relative modular classes of Lie algebroids, C. R. Acad. Sci. Paris, Ser. I, 341 (2005), 509-514, math.DG/0508515.

Derived brackets, Lett. Math. Phys., 69 (2004), 61-87, mathDG/0312524.

Quasi, twisted, and all that... in Poisson geometry and Lie algebroid theory, The Breadth of Symplectic and Poisson Geometry, Festschrift in honor of Alan Weinstein, Progress in Mathematics 232, eds. J. E. Marsden and T. Ratiu, Birkhauser, 2005, 363-389, mathSG/0310359.

With K. C. H. Mackenzie, Differential operators and actions of Lie algebroids, Quantization, Poisson Brackets and Beyond, ed. Theodore Voronov, Contemp. Math. 315 (2002), Amer. Math. Soc., Providence, R.I., 213-233, math.DG/0209337.

With J. Monterde, Divergence operators and odd Poisson brackets, Ann. Inst. Fourier, Grenoble, 52(2) (2002), p. 419-456, math.QA/0002209.

With A. Alekseev and E. Meinrenken, Quasi-Poisson manifolds, Canadian J. Math., 54(1) (2002), 3-29, math.DG/0006168.

With A. Alekseev, Manin pairs and moment maps, J. Diff. Geometry, 56 (2000), 133-165, math.DG/9909176.

Modular vector fields and Batalin-Vilkovisky algebras, in Poisson Geometry, eds. J. Grabowski and P. Urbanski, Banach Center Publications, 51 (2000), 109-129.

With B. Enriquez, Quantum homogeneous spaces and quasi-Hopf algebras, Conférence Moshé Flato 1999, vol. 2, eds. G. Dito and D. Sternheimer, Kluwer, Dordrecht, 2000, 105-121, math.QA/9912243.

Odd and even Poisson brackets, in Quantum Theory and Symmetries, eds. H.-D. Doebner, V. K. Dobrev, J.-D. Hennig and W. Lücke, World Scientific, Singapore, 2000, 565-571.

"Lie algebroid'', Encyclopaedia of Mathematics, Supplement II, Kluwer, Dordrecht, 2000, 309-311. Available online here.

"Loday algebra (Leibniz algebra)'', Encyclopaedia of Mathematics, Supplement II, Kluwer, Dordrecht, 2000, 318-319. Available online here.

With M. Bangoura, Équation de Yang-Baxter dynamique classique et algébroïdes de Lie, Comptes rendus Acad. Sci., Paris, 237, Série I (1998), 541-546.

Spinning Tops, The Stamp Corner, The Mathematical Intelligencer, 20 (4) (1998), 65.

Derived brackets and the gauge Lie algebra of closed string theory, in Quantum Group Symposium at Group 21, eds. H.-D. Doebner and V. K. Dobrev, Heron Press, Sofia, 1997, 53-61.

Lie bialgebras, Poisson Lie groups and dressing transformations, Integrability of Nonlinear Systems (Proc. CIMPA School, Pondicherry University 1996), eds., Y. Kosmann-Schwarzbach, B. Grammaticos and K. M. Tamizhmani, Lect. Notes Phys., 495, Springer-Verlag, Berlin, 1997, 104-170. Second, revised edition: Lecture Notes in Physics, 638, Springer-Verlag, Berlin, 2004, 107-173.

"Poisson algebra'', Encyclopaedia of Mathematics, Supplement I, Kluwer, Dordrecht, 1997, 413-414. Available online here.

"Poisson Lie group'', Encyclopaedia of Mathematics, Supplement I, Kluwer, Dordrecht, 1997, 414-415. Available online here.

The Lie bialgebroid of a Poisson-Nijenhuis manifold, Lett. Math. Phys., 38 (1996), 421- 428.

With F. Magri, Lax-Nijenhuis operators for integrable systems, J. Math. Phys., 37 (12) (1996), 6173-6197.

From Poisson algebras to Gerstenhaber algebras, Ann. Inst. Fourier, Grenoble 46 (5) (1996), 1243- 1274.

Poisson-Lie groups and beyond, J. Math. Sciences, 82 (6) (1996), 3807-3813 (traduit de Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, 21, Algebra-3, 1995).

Exact Gerstenhaber algebras and Lie bialgebroids, Acta Appl. Math. 41 (1995), 153-165.

Graded Poisson brackets and field theory, Modern Group Theoretical Methods in Physics, eds., J. Bertrand, M. Flato, J.-P. Gazeau, M. Irac-Astaud and D. Sternheimer, Kluwer, Dordrecht, 1995, 189-196.

With M. Bangoura, The double of a Jacobian Lie bialgebra, Lett. Math. Physics, 28 (1993), 13-29.

Jacobian quasi-bialgebras and quasi-Poisson Lie groups, Mathematical Aspects of Classical Field Theory, eds., M. Gotay, J. E. Marsden and V. Moncrief, Contemporary Mathematics 132, American Mathematical Society, 1992, 459-489.

Quasi-bigèbres de Lie et groupes de Lie quasi-Poisson, Comptes rendus Acad. Sci., Paris, 312, Série I (1991), 391-394.

Champs affines de multivecteurs sur les groupes de Lie, Comptes rendus Acad. Sci., Paris, 312, Série I (1991), 233-236.

Grand crochet, crochets de Schouten et cohomologies d'algèbres de Lie, Comptes rendus Acad. Sci., Paris, 312, Série I (1991), 123-126.

From ``Quantum Groups'' to ``Quasi-Quantum Groups'', Symmetries in Science V, Algebraic Systems, their Representations, Realizations and Physical Applications, eds., B. Gruber, L. C. Biedenharn and H. D. Doebner, Plenum, New York, 1991, 369-393.

Groupes de Lie-Poisson quasitriangulaires, Géométrie symplectique et mécanique (Colloque international, La Grande-Motte 1988), éd., C. Albert, Lecture Notes Math. 1416, Spinger-Verlag, Berlin, 1990, 161-177.

With F. Magri, Dualization and deformation of Lie brackets on Poisson manifolds, Differential Geometry and its Applications (Conférence internationale, Brno 1989), eds., J. Janyska and D. Krupka, World Scientific, Singapore, 1990, 79-84.

With F. Magri, Poisson-Nijenhuis structures, Ann. Inst. Henri Poincaré, Série A, 53 (1990), 35-81.

Generalized symmetries, recursion operators and bihamiltonian systems, Partially integrable nonlinear evolution equations and their physical applications (Les Houches, 1989), eds., R. Conte and N. Boccara, NATO ASI series C, 310, Kluwer, Dordrecht, 1990, 479-489.

Quantum and classical Yang-Baxter equations, Modern Physics Letters A, 5, no. 13 (1990), 981-990.

The modified Yang-Baxter equation and bihamiltonian structures, Differential Geometric Methods in Theoretical Physics, éd., A. I. Solomon, World Scientific, Singapore, 1989, 12-25.

With R. Aminou, Bigèbres de Lie, doubles et carrés, Ann. Inst. Henri Poincaré, Série A, 49 (1988), 461-478.

With F. Magri, Poisson-Lie groups and complete integrability, I. Drinfeld bigebras, dual extensions and their canonical representations, Ann. Inst. Henri Poincaré, Série A, 49 (1988), 433-460.

Sur les théorèmes de Noether, Géométrie et physique, eds., Y. Choquet-Bruhat, B. Coll, R. Kerner and A. Lichnerowicz, Coll. Travaux en cours no. 21 , Hermann, Paris, 1987, 147-160.

Equations de Yang-Baxter et structures de Poisson, Journées Relativistes de Chambéry, Université de Savoie, 1987, 79-93.

Poisson-Drinfeld groups, Topics in soliton theory and exactly solvable nonlinear equations, éd., M. Ablowitz, B. Fuchssteiner, M. Kruskal, World Scientific, Singapore, 1987, 191-215.

Géométrie des systèmes bihamiltoniens, Systèmes dynamiques non linéaires: intégrabilité et comportement qualitatif, éd., P. Winternitz, Séminaire de Mathématiques Supérieures, 102, Presses de l'Université de Montréal, 1986, 185-216.

On the momentum mapping in field theory, Differential geometric methods in mathematical physics (Clausthal 1983), eds., H. D. Doebner et J.D. Hennig, Lecture Notes in Math., 1139, Springer-Verlag, Berlin, 1985, 25-73.

Lagrangian foliations and Lax equations, Lett. Math. Phys., 9 (1985), 163-167.

Lie algebras of symmetries of partial differential equations, Differential geometric methods in mathematical physics (Jérusalem 1982), éd., S. Sternberg, Reidel, Dordrecht, 1984, 241-277.

With T. P. Branson, Conformally covariant nonlinear equations on tensor- spinors, Lett. Math. Phys., 7 (1983), 63-73.

Hamiltonian systems on fibered manifolds (Poisson and vertical brackets in field theory), Lett. Math. Phys., 5 (1981), 229-237.

Generalized symmetries of partial differential equations, Group theoretical methods in physics (Proc. VIIIth Int. Coll., Kiriat Anavim, Israël, 1979), eds., L. A. Horowitz and Y. Ne'eman, Ann. Isr. Phys. Soc., 3 (1980), 342-344.

Vector fields and generalized vector fields on fibered manifolds, Geometry and differential geometry (Proc. Conf. Univ. Haifa, Israël, 1979), eds., R. Artzy and I. Vaisman, Lecture Notes in Math., 792, Springer-Verlag, Heidelberg, 1980, 307-355.

Infinitesimal conditions for the equivariance of morphisms of fibered manifolds, Proc. Amer. Math. Soc., 77 (1979), 374-380.

Generalized symmetries of nonlinear partial differential equations, Lett. Math. Phys., 3 (1979), 395-404.

Dérivées de Lie des morphismes de fibrés, Publ. math. Univ. Paris VII, 3 (1978), 55-72.

Sur les transformations de similitude des équations aux dérivées partielles, Comptes rendus Acad. Sci., Paris, 287, Série A (1978), 953-956.

On Lie transformation groups and the covariance of differential operators, Differential Geometry and Relativity, eds., M. Cahen and M. Flato, Reidel, Dordrecht, 1976, 75-89.

Degrés conformes des laplaciens et des opérateurs de Dirac, Comptes rendus Acad. Sci., Paris, 280, Série A (1975), 283-285.

Sur les degrés conformes des opérateurs différentiels, Comptes rendus Acad. Sci., Paris, 280, Série A (1975), 229-232.

Sur la notion de covariance en relativité générale, Journées relativistes, Univ. de Dijon (1975).

Covariance conforme d'opérateurs en relativité générale, Colloque de géométrie différentielle du FNRS, Univ. Libre de Bruxelles (1974).

With S. Sternberg, Conjugaison des sous-algèbres d'isotropie, Comptes rendus Acad. Sci., Paris, 279, Série A (1974), 777-779.

Représentations semi-linéaires et covariance, Publ. interne no. 19, UER de Math., Univ. des Sciences et Tech. de Lille (1973).

Groupes de transformations et covariance des opérateurs différentiels, Comptes rendus. Acad. Sci., Paris, 275, Série A (1972), 1235-1237.

Dérivées de Lie des spineurs (thèse), Ann. Mat. pura appl., IV, 91 (1972), 317-395.

Propriétés des dérivations de l'algèbre des tenseurs-spineurs, Comptes rendus Acad. Sci., Paris, 264, Série A (1967), 355-358.

Dérivées de Lie des spineurs. Applications, Comptes rendus Acad. Sci., Paris, 262, Série A (1966), 394-397

Dérivées de Lie des spineurs, Comptes rendus Acad. Sci., Paris, 262, Série A (1966), 289-292.