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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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Book Review

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MathSciNet review: 2594632
Full text of review: PDF   This review is available free of charge.
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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  • J. N. Bernstein and S. I. Gel′fand, Tensor products of finite- and infinite-dimensional representations of semisimple Lie algebras, Compositio Math. 41 (1980), no. 2, 245–285. MR 581584
  • I. N. Bernšteĭn, I. M. Gel′fand, and S. I. Gel′fand, A certain category of ${\mathfrak {g}}$-modules, Funkcional. Anal. i Priložen. 10 (1976), no. 2, 1–8 (Russian). MR 0407097
  • Jacques Dixmier, Algèbres enveloppantes, Cahiers Scientifiques, Fasc. XXXVII, Gauthier-Villars Éditeur, Paris-Brussels-Montreal, Que., 1974 (French). MR 0498737
  • Jens Carsten Jantzen, Moduln mit einem höchsten Gewicht, Lecture Notes in Mathematics, vol. 750, Springer, Berlin, 1979 (German). MR 552943
  • Jens Carsten Jantzen, Einhüllende Algebren halbeinfacher Lie-Algebren, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 3, Springer-Verlag, Berlin, 1983 (German). MR 721170, DOI 10.1007/978-3-642-68955-0
  • Robert V. Moody and Arturo Pianzola, Lie algebras with triangular decompositions, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, Inc., New York, 1995. A Wiley-Interscience Publication. MR 1323858
  • 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, DOI 10.1215/S0012-7094-04-12634-X

  • 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
    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.