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Book review: General theory of Lie groupoids and Lie algebroids, by Kirill C. H. Mackenzie

Reprinted with permission. Originally published as: Theodore Voronov, Book review: General theory of Lie groupoids and Lie algebroids (London Mathematical Society Lecture Note Series 213) By Kirill C. H. Mackenzie: xxxviii+501 pp., £50.00 (US$90.00) (LMS members' price £37.50 (US$67.50)), isbn 0-521-49928-3 (Cambridge University Press, Cambridge, 2005). Bull. Lond. Math. Soc. 42 (2010), no. 1,185–190. © 2010 London Mathematical Society. doi: 10.1112/blms/bdp115. Published online 5 January 2010.

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  • [1] M. F. Atiyah, Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc., 85 (1957), 181-207.  doi: 10.1090/S0002-9947-1957-0086359-5.
    [2] H. Brandt, Über eine Verallgemeinerung des Gruppenbegriffes, Math. Ann., 96 (1927), 360-366.  doi: 10.1007/BF01209171.
    [3] R. Brown, From groups to groupoids: A brief survey, Bull. London Math. Soc., 19 (1987), 113–134, Extended version at http://www.bangor.ac.uk/r.brown/groupoidsurvey.pdf. doi: 10.1112/blms/19.2.113.
    [4] A. Cannas da Silva and A. Weinstein, Geometric Models for Noncommutative Algebras, American Mathematical Society, Providence, RI, 1999.
    [5] A. S. Cattaneo and G. Felder, A path integral approach to the Kontsevich quantization formula, Comm. Math. Phys., 212 (2000), 591-611.  doi: 10.1007/s002200000229.
    [6] A. Connes, Noncommutative Geometry, Academic Press Inc., San Diego, CA, 1994.
    [7] M. Crainic and R. L. Fernandes, Integrability of Lie brackets, Ann. of Math. (2), 157 (2003), 575-620.  doi: 10.4007/annals.2003.157.575.
    [8] C. Ehresmann, Œuvres complètes et commentées. I-1, 2. Topologie algébrique et géométrie différentielle, Cahiers Topologie Géom. Différentielle, 24 (1983).
    [9] J.-C. Herz, Pseudo-algèbres de Lie. I, C. R. Acad. Sci. Paris, 236 (1953), 1935-1937. 
    [10] P. J. Higgins and K. Mackenzie, Algebraic constructions in the category of Lie algebroids, J. Algebra, 129 (1990), 194-230.  doi: 10.1016/0021-8693(90)90246-K.
    [11] M. V. Karasëv, Analogues of objects of the theory of Lie groups for nonlinear Poisson brackets, Izv. Akad. Nauk SSSR Ser. Mat., 50 (1986), 508-538. 
    [12] K. MackenzieLie Groupoids and Lie Algebroids in Differential Geometry, Cambridge University Press, Cambridge, 1987.  doi: 10.1017/CBO9780511661839.
    [13] K. C. H. Mackenzie, Lie algebroids and Lie pseudoalgebras, Bull. London Math. Soc., 27 (1995), 97-147.  doi: 10.1112/blms/27.2.97.
    [14] K. C. H. Mackenzie, Ehresmann doubles and Drinfel'd doubles for Lie algebroids and Lie bialgebroids, De Gruyter, 2011 (2011). doi: 10.1515/crelle.2011.092.
    [15] K. C. H. Mackenzie and P. Xu, Lie bialgebroids and Poisson groupoids, Duke Math. J., 73 (1994), 415-452.  doi: 10.1215/S0012-7094-94-07318-3.
    [16] I. Moerdijk and  J. MrčunIntroduction to Foliations and Lie Groupoids, Cambridge University Press, Cambridge, 2003.  doi: 10.1017/CBO9780511615450.
    [17] J. Pradines, Théorie de Lie pour les groupoï des différentiables. Calcul différenetiel dans la catégorie des groupoï des infinitésimaux, C. R. Acad. Sci. Paris Sér. A-B, 264 (1967), A245–A248.
    [18] J. Pradines, Géométrie différentielle au-dessus d'un groupoï de, C. R. Acad. Sci. Paris Sér. A-B, 266 (1968), A1194–A1196.
    [19] J. Pradines, Troisième théorème de Lie les groupoï des différentiables, C. R. Acad. Sci. Paris Sér. A-B, 267 (1968), A21–A23.
    [20] T. Voronov, Q-manifolds and Mackenzie theory: An overview, preprint, arXiv: 0709.4232, [math.DG]. ESI 1952, 2007.
    [21] A. Weinstein, Symplectic groupoids and Poisson manifolds, Bull. Amer. Math. Soc. (N.S.), 16 (1987), 101-104.  doi: 10.1090/S0273-0979-1987-15473-5.
    [22] A. Weinstein, Groupoids: Unifying internal and external symmetry. A tour through some examples, Notices Amer. Math. Soc., 43 (1996), 744-752. 
    [23] S. Zakrzewski, Quantum and classical pseudogroups. Ⅰ. Union pseudogroups and their quantization, Comm. Math. Phys., 134 (1990), 347-370.  doi: 10.1007/BF02097706.
    [24] S. Zakrzewski, Quantum and classical pseudogroups. Ⅱ. Differential and symplectic pseudogroups, Comm. Math. Phys., 134 (1990), 371-395.  doi: 10.1007/BF02097707.
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