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Book Review
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Book Information
Author(s):
Robert V. Moody and Arturo Pianzola
Title:
Lie algebras with triangular decompositions
Additional book information:
Canad. Math. Soc. Ser. Monographs Adv. Texts, Wiley-Interscience,
New York,
1995,
xx + 685,
ISBN 0-471-63304-6
References:
- 1.
- Serre, J.-P., Algèbres de Lie semi-simples complexes, Benjamin, New York, 1966. MR 35:6721
- 2.
- Humphreys, J. E., Introduction to Lie algebras and representation theory, Springer, New York, 1972. MR 48:2197
- 3.
- Gabber, O., and Kac, V. G., On defining relations of certain infinite-dimensional Lie algebras, Bull. Amer. Math. Soc. (N.S.) 5 (1981), 185--189. MR 84b:17011
- 4.
- Kac, V. G., Simple irreducible graded Lie algebras of finite growth, Izv. Akad. Nauk SSSR 32 (1968), 1323--1367; English transl., Math. USSR-Izv. 2 (1968), 1271--1311. MR 41:4590
- 5.
- Moody, R. V., A new class of Lie algebras, J. Algebra 10 (1968), 211--230. MR 37:5261
- 6.
- Kac, V. G., and Peterson, D. H., Infinite-dimensional Lie algebras, theta functions and modular forms, Adv. in Math. 53 (1984), 125--264. MR 86a:17007
- 7.
- Kac, V. G. and Kazhdan, D. A., The structure of representations with highest weight of infinite-dimensional Lie algebras, Adv. in Math. 34 (1979), 97--108. MR 81d:17004
- 8.
- Bernstein, I. N., Gelfand, I. M., and Gelfand, S. I., Structure of representations generated by vectors of highest weight, Funktsional Anal. i Prilozhen 5 (1971), 1--9; English transl., Functional Anal. Appl. 5 (1971), 1--8. MR 45:298
- 9.
- Kac, V. G., and Wakimoto, M., Modular invariant representations of infinite dimensional Lie algebras and superalgebras, Proc. Nat. Acad. Sci. U.S.A. 85 (1988), 4956--4960. MR 89j:17019
- 10.
- Tits, J., Groupes associés aux algèbres de Kac-Moody. Séminaire Bourbaki, Nov. 1988, Astérisque 177-178 (1988--89), 7--31. MR 91c:22034
- 11.
- Kac, V. G., Infinite dimensional Lie algebras, 3rd. ed., Cambridge Univ. Press, Cambridge, 1990. MR 92k:17038
Additional Information:
Reviewer(s):
George
B.
Seligman
Affiliation:
Yale University
Email:
selig@math.yale.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
33
(1996),
347-349.
MSC
(1991):
Primary 17B67;
Secondary 17B65
DOI:
10.1090/S0273-0979-96-00653-2
PII:
S 0273-0979(96)00653-2
Copyright of article:
Copyright
1996,
American Mathematical Society
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