Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

MathSciNet review: 1214142
Full text of review: PDF   This review is available free of charge.
Book Information:

Author: N. V. Karasev and V. P. Maslov
Title: Nonlinear Poisson brackets, geometry and quantization
Additional book information: Translations of Math. Monographs, vol. 119, Amer. Math. Soc., Providence, RI, 1993, xi + 366 pp., ISBN 0-8218-4596-9, $170.00$

References [Enhancements On Off] (What's this?)

  • Claude Albert and Pierre Dazord, Groupoïdes de Lie et groupoïdes symplectiques, Symplectic geometry, groupoids, and integrable systems (Berkeley, CA, 1989) Math. Sci. Res. Inst. Publ., vol. 20, Springer, New York, 1991, pp. 1–11 (French). MR 1104916, DOI 10.1007/978-1-4613-9719-9_{1}
  • Leo F. Epstein, A function related to the series for $e^{e^x}$, J. Math. Phys. Mass. Inst. Tech. 18 (1939), 153–173. MR 58, DOI 10.1002/sapm1939181153
  • Élie Cartan, Leçons sur les invariants intégraux, Hermann, Paris, 1971 (French). Troisième tirage. MR 0355764
  • Alain Connes, Géométrie non commutative, InterEditions, Paris, 1990 (French). MR 1079062
  • A. Coste, P. Dazord, and A. Weinstein, Groupoïdes symplectiques, Publications du Département de Mathématiques. Nouvelle Série. A, Vol. 2, Publ. Dép. Math. Nouvelle Sér. A, vol. 87, Univ. Claude-Bernard, Lyon, 1987, pp. i–ii, 1–62 (French). MR 996653
  • P. Dazord and G. Hector, Intégration symplectique des variétés de Poisson totalement asphériques, Symplectic geometry, groupoids, and integrable systems (Berkeley, CA, 1989) Math. Sci. Res. Inst. Publ., vol. 20, Springer, New York, 1991, pp. 37–72 (French, with English summary). MR 1104919, DOI 10.1007/978-1-4613-9719-9_{4}
  • P. Dazord and G. Patissier, La première classe de Chern comme obstruction à la quantification asymptotique, Symplectic geometry, groupoids, and integrable systems (Berkeley, CA, 1989) Math. Sci. Res. Inst. Publ., vol. 20, Springer, New York, 1991, pp. 73–97 (French). MR 1104920, DOI 10.1007/978-1-4613-9719-9_{5}
  • Marc De Wilde and Pierre B. A. Lecomte, Existence of star-products and of formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds, Lett. Math. Phys. 7 (1983), no. 6, 487–496. MR 728644, DOI 10.1007/BF00402248
  • C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13
  • M. V. Karasëv, Analogues of objects of the theory of Lie groups for nonlinear Poisson brackets, Izv. Akad. Nauk SSSR Ser. Mat. 50 (1986), no. 3, 508–538, 638 (Russian). MR 854594
  • J. L. Walsh, On interpolation by functions analytic and bounded in a given region, Trans. Amer. Math. Soc. 46 (1939), 46–65. MR 55, DOI 10.1090/S0002-9947-1939-0000055-0
  • Bertram Kostant, Quantization and unitary representations. I. Prequantization, Lectures in modern analysis and applications, III, Lecture Notes in Math., Vol. 170, Springer, Berlin, 1970, pp. 87–208. MR 0294568
  • Paulette Libermann, Problèmes d’équivalence et géométrie symplectique, Third Schnepfenried geometry conference, Vol. 1 (Schnepfenried, 1982) Astérisque, vol. 107, Soc. Math. France, Paris, 1983, pp. 43–68 (French). MR 753129
  • Paulette Libermann and Charles-Michel Marle, Symplectic geometry and analytical mechanics, Mathematics and its Applications, vol. 35, D. Reidel Publishing Co., Dordrecht, 1987. Translated from the French by Bertram Eugene Schwarzbach. MR 882548, DOI 10.1007/978-94-009-3807-6
  • André Lichnerowicz, Les variétés de Poisson et leurs algèbres de Lie associées, J. Differential Geometry 12 (1977), no. 2, 253–300 (French). MR 501133
  • J.-M. Souriau, Structure des systèmes dynamiques, Dunod, Paris, 1970 (French). Maîtrises de mathématiques. MR 0260238
  • Izu Vaisman, Lectures on the geometry of Poisson manifolds, Progress in Mathematics, vol. 118, Birkhäuser Verlag, Basel, 1994. MR 1269545, DOI 10.1007/978-3-0348-8495-2
  • Alan Weinstein, The local structure of Poisson manifolds, J. Differential Geom. 18 (1983), no. 3, 523–557. MR 723816
  • Alan Weinstein, Symplectic groupoids and Poisson manifolds, Bull. Amer. Math. Soc. (N.S.) 16 (1987), no. 1, 101–104. MR 866024, DOI 10.1090/S0273-0979-1987-15473-5
  • Alan Weinstein, Noncommutative geometry and geometric quantization, Symplectic geometry and mathematical physics (Aix-en-Provence, 1990) Progr. Math., vol. 99, Birkhäuser Boston, Boston, MA, 1991, pp. 446–461. MR 1156554
  • Alan Weinstein and Ping Xu, Extensions of symplectic groupoids and quantization, J. Reine Angew. Math. 417 (1991), 159–189. MR 1103911

  • Review Information:

    Reviewer: P. Libermann
    Affiliation: University Paris VII
    Journal: Bull. Amer. Math. Soc. 33 (1996), 101-105
    Review copyright: © Copyright 1996 American Mathematical Society