Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
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
Joseph Bernstein, Igor Frenkel, and Mikhail Khovanov, A categorification of the Temperley-Lieb algebra and Schur quotients of $U(\mathfrak {sl}_2)$ via projective and Zuckerman functors, Selecta Math. (N.S.) 5 (1999), no. 2, 199–241. MR 1714141, DOI 10.1007/s000290050047
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
References
- Joseph Bernstein, Igor Frenkel, and Mikhail Khovanov, A categorification of the Temperley-Lieb algebra and Schur quotients of $U( {\mathfrak {sl}}_ 2)$ via projective and Zuckerman functors, Selecta Math. (N.S.) 5 (1999), no. 2, 199–241. MR 1714141 (2000i:17009)
- 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)
- 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)
- Jacques Dixmier, Algèbres enveloppantes, Cahiers Scientifiques, Gauthier-Villars, 1974. MR 0498737 (58:16803a)
- Jens Carsten Jantzen, Moduln mit einem höchsten Gewicht, Lecture Notes in Mathematics, vol. 750, Springer, 1979. MR 552943 (81m:17011)
- —, Einhüllende Algebren halbeinfacher Lie-Algebren, Ergebnisse der Mathematik, vol. 3, Springer, 1983. MR 721170 (86c:17011)
- Robert V. Moody and Arturo Pianzola, Lie algebras with triangular decompositions, John Wiley & Sons, New York, 1995. MR 1323858 (96d:17025)
- 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
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.
