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Book Review

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Book Information:

Author: James E. Humphreys
Title: Representations of semisimple Lie algebras in the BGG category $ \mathcal O$
Additional book information: Graduate Studies in Mathematics, Vol. 94, American Mathematical Society, Providence, RI, 2008, xvi+289 pp., ISBN 978-0-8218-4678-0

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

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  • [BG80] Joseph N. Bernstein and Sergei I. Gelfand, Tensor products of finite and infinite representations of semisimple Lie algebras, Compositio Math. 41 (1980), 245-285. MR 581584 (82c:17003)
  • [BGG76] Joseph N. Bernstein, Israel M. Gelfand, and Sergei I. Gelfand, Category of $ {\mathfrak{g}}$-modules, Functional Analysis and its Applications 10 (1976), 87-92. MR 0407097 (53:10880)
  • [Dix74] Jacques Dixmier, Algèbres enveloppantes, Cahiers Scientifiques, Gauthier-Villars, 1974. MR 0498737 (58:16803a)
  • [Jan79] Jens Carsten Jantzen, Moduln mit einem höchsten Gewicht, Lecture Notes in Mathematics, vol. 750, Springer, 1979. MR 552943 (81m:17011)
  • [Jan83] -, Einhüllende Algebren halbeinfacher Lie-Algebren, Ergebnisse der Mathematik, vol. 3, Springer, 1983. MR 721170 (86c:17011)
  • [MP95] Robert V. Moody and Arturo Pianzola, Lie algebras with triangular decompositions, John Wiley & Sons, New York, 1995. MR 1323858 (96d:17025)
  • [Str05] Catharina Stroppel, Categorification of the Temperley-Lieb category, tangles, and cobordisms via projective functors, Duke Math. J. 126 (2005), no. 3, 547-596. MR 2120117 (2005i:17011)

Review Information:

Reviewer: Wolfgang Soergel
Affiliation: Mathematisches Institut Albert-Ludwigs-Universität Freiburg, Germany
Email: wolfgang.soergel@math.uni-freiburg.de
Journal: Bull. Amer. Math. Soc. 47 (2010), 367-371
MSC (2000): Primary 17B10; Secondary 20G05, 22E47
DOI: https://doi.org/10.1090/S0273-0979-09-01266-X
Published electronically: July 13, 2009
Review copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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