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ISSN 1088-9485(e) ISSN 0273-0979(p)

Book Review

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Book Information

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

References:

[BFK99]: Joseph Bernstein, Igor Frenkel, and Mikhail Khovanov, A categorification of the Temperley-Lieb algebra and Schur quotients of $U( {\mathfrak{sl}}\sb 2)$ via projective and Zuckerman functors, Selecta Math. (N.S.) 5 (1999), no. 2, 199-241. MR 1714141 (2000i:17009)
[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)

Additional Information:

Reviewer(s):
Wolfgang Soergel
Affiliation: Mathematisches Institut Albert-Ludwigs-Universität Freiburg, Germany
Email: wolfgang.soergel@math.uni-freiburg.de

Review Information:
Journal: Bull. Amer. Math. Soc. 47 (2010), 367-371.

MSC (2000): Primary 17B10; Secondary 20G05, 22E47
DOI: 10.1090/S0273-0979-09-01266-X
PII: S 0273-0979(09)01266-X
Posted: July 13, 2009
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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