@article{AIHPA_1990__53_1_35_0,
author = {Kosmann-Schwarzbach, Yvette and Magri, Franco},
title = {Poisson-Nijenhuis structures},
journal = {Annales de l'I.H.P. Physique th\'eorique},
pages = {35--81},
year = {1990},
publisher = {Gauthier-Villars},
volume = {53},
number = {1},
mrnumber = {1077465},
zbl = {0707.58048},
language = {en},
url = {https://www.numdam.org/item/AIHPA_1990__53_1_35_0/}
}
Kosmann-Schwarzbach, Yvette; Magri, Franco. Poisson-Nijenhuis structures. Annales de l'I.H.P. Physique théorique, Tome 53 (1990) no. 1, pp. 35-81. https://www.numdam.org/item/AIHPA_1990__53_1_35_0/
[1] and , Kowalewski's asymptotic method, Kac-Moody Lie algebras and regularization, Comm. Math. Phys., T. 83, 1982, pp. 83-106. | Zbl | MR
[2] , Groupes de Lie-Poisson et bigèbres de Lie, Thèse, Université des Sciences et Techniques de Lille Flandres Artois, June 1988.
[3] and , Calculus on Poisson manifolds, Bull. London Math. Soc., T. 20, 1988, pp. 68-72. | Zbl | MR
[4] K. H, BHASKARA and , Poisson algebras and Poisson manifolds, Pitman Research Notes in Math., Longman, 1988. | Zbl | MR
[5] , Structures (K, A)-linéaires, C. R. Acad. Sci. Paris, T. 262, série A, 1966, pp. 373-376. | Zbl | MR
[6] , A differential complex for Poisson manifolds, J. Differential Geometry, T. 28, 1988, pp. 93-114. | Zbl | MR
[7] , Les dérivations des champs de tenseurs et l'invariant différentiel de Schouten, C. R. Acad. Sci. Paris, T. 269, série A, 1969, pp. 87-89. | Zbl | MR
[8] , On some involution theorems on twofold Poisson manifolds, Lett. Math. Physics, T. 15, 1988, pp. 193-200. | Zbl | MR
[9] , and , Groupoïdes symplectiques, Publ. Dép. Math. Université de Lyon-I, 2/A, 1987. | Zbl | Numdam
[10] , Espaces infinitésimaux, Cahiers Topol. Géom. Diff., T. 7, 1965. | EuDML | Zbl | Numdam
[11] , Opérateurs infinitésimaux sur l'algèbre des formes différentielles extérieures, C. R. Acad. Sci. Paris, T. 261, Groupe 1, 1965, pp. 4594-4597. | Zbl | MR
[12] , Deformations of Hamiltonian structures and integrable systems, in Nonlinear phenomena and turbulence, Gordon and Breach, 1984. | MR
[13] , The Toda lattice in the complex domain, in Algebraic Analysis, in honor of Sato, M. KASHIWARA and T. KAWAI Eds., Vol. 1, Academic Press, 1988. | Zbl | MR
[14] and , Theory of vector-valued differential forms, Part I. Derivations in the graded ring of differential forms, Indag. Math., T. 18, 1956, pp. 338- 350 and 351-359. | Zbl | MR
[15] and , Hamiltonian operators and the classical Yang-Baxter equation, Funct. Anal. Appl., T. 16, No. 4. 1982, pp. 241-248. | Zbl | MR
[16] , Pseudo-algèbres de Lie, C. R. Acad. Sci. Paris, T. 236, 1953, I, pp. 1935- 1937 and II, pp. 2289-2291. | Zbl
[17] , Functional Analysis, Wiley, New York 1982. | Zbl
[18] , Poison cohomology and quantization, J. für die Reine und Angew. Math. (to appear). | Zbl | MR | EuDML
[19] , Analogues of the objects of Lie group theory for nonlinear Poisson brackets, Math. U.S.S.R. Izvestiya, T. 28, No. 3, 1987, pp. 497-527 (in Russian, Izvestiya, T. 50, 1986). | Zbl | MR
[20] and , Lie-Cartan pairs, J. Geom. and Physics, T. 2, No. 3, 1985. | Zbl | MR
[21] and , Poisson-Lie groups and complete integrability, Part I. Drinfeld bigebras, dual extensions and their canonical representations, Ann. Inst. Henri Poincaré, série A (Physique théorique), T. 49, No. 4, 1988, pp. 433- 460, Parts II and III in preparation. | Numdam | Zbl | MR | EuDML
[21 a] , The modified Yang-Baxter equation and bihamiltonian structures, in Differential Geometric Methods in Theoretical Physics (Chester, August 1988), A. SOLOMON Ed., World Scientific, Singapore, 1989, pp. 12-25. | MR
[22] , The solution to a generalized Toda lattice and representation theory, Adv. in Math., T. 34, 1979, pp. 195-338. | Zbl | MR
[23] , Crochet de Schouten-Nijenhuis et cohomologie, in Elie Cartan et les mathématiques d'aujourd'hui, Société Mathématique de France, Astérisque, hors série, 1985, pp. 257-271. | Zbl | MR | Numdam
[24] , Schouten bracket and canonical algebras, in Global Analysis III, Lect. Notes Math., No. 1334, 1988, pp. 79-110. | Zbl | MR
[25] , Étude des formes différentielles liées à certaines G-structures, C. R. Acad. Sci. Paris, T. 260, Groupe 1, 1965, pp. 1838-1841. | Zbl | MR
[26] , Intégrabilité des G-structures définies par une 1-forme 0-déformable à valeurs dans le fibré tangent, Ann. Inst. Fourier, Grenoble, T. 16, No. 2, 1966, pp. 329-387. | Numdam | Zbl | MR | EuDML
[27] , Les variétés de Poisson et leurs algèbres de Lie associées, J. Diff. Geom., T. 12, 1977, pp. 253-300. | Zbl | MR
[28] and , Poisson Lie groups, dressing transformations and Bruhat decompositions, J. Diff. Geometry, T. 31, 1990, pp. 501-526. | Zbl | MR
[29] , Lie groupoids and Lie algebroids in Differential Geometry, London Math. Soc. Lect. Notes, No. 124, Cambridge University Press, 1987. | Zbl
[30] and , A geometrical characterization of integrable Hamiltonian systems through the theory of Poisson-Nijenhuis manifolds, Quaderno, S 19, 1984, University of Milan.
[31] , and , Reduction techniques for infinite-dimensional Hamiltonian systems: Some ideas and applications, Comm. Math. Phys., T. 99, 1985, pp. 115-140. | Zbl | MR
[31 a] , Geometry and soliton equations, in La Mécanique Analytique de Lagrange et son héritage, Collège de France, September 1988 (to appear). | MR
[32] , Non-commutative-geometric Groups by a Bicrossproduct construction: Hopf algebras at the Planck scale, Ph. D. Thesis, Harvard University, August 1988.
[33] , Remarks on the Schouten-Nijenhuis bracket, Rendiconti Circ. Mat. Palermo (2), Suppl. No. 16, 1987, pp. 207-215. | Zbl | MR
[34] , Tensor Analysis, Princeton University Press, 1967. | Zbl
[35] and , Deformations of Lie algebra structures, J. Math. and Mech., T. 17, No. 1, 1967, pp. 89-105. | Zbl | MR
[36] , Hamiltonian actions on Poisson manifolds, in Symplectic Geometry, A. CRUMEYROLLE and J. GRIFONE Eds., Research Notes in Math., No. 80, Pitman, 1983. | Zbl | MR
[37] , The Cohomology of Lie rings, Proc. Symp. Pure Math., 3, Amer. Math. Soc., 1961, pp. 130-137. | Zbl | MR
[38] , Théorie de Lie pour les groupoides différentiables. Calcul différentiel dans la catégorie des groupoïdes infinitésimaux, C. R. Acad. Sci. Paris, T. 264, série A, 1967, pp. 245-248. | Zbl | MR
[39] , Differential forms on general commutative algebras, Trans. Amer. Math. Soc., T. 108, 1963, p. 195-222. | Zbl | MR
[40] , On the differential operators of first order in tensor calculus, Conv. di Geom. Differen., 1953, Cremonese, Rome, 1954. | Zbl | MR
[41] , What is a classical r-matrix?, Funct. Anal. Appl., T. 17, No. 4, 1983, pp. 259-272. | Zbl
[42] , Some remarks on dressing transformations, J. Fac. Sci. Univ. Tokyo, Sect. 1 A, Math., T. 36, 1988, pp. 163-167. | Zbl | MR
[43] , Integrability of generalized Toda lattice systems and singularities in the complex t-plane, in Nonlinear Integrable Systems, Classical Theory and Quantum Theory, World Scientific, Singapore, 1983. | Zbl | MR





