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Book Review

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Book Information:

Authors: 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 pp., ISBN 0-471-63304-6

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

  • 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

Review Information:

Reviewer: George B. Seligman
Affiliation: Yale University
Email: selig@math.yale.edu
Journal: Bull. Amer. Math. Soc. 33 (1996), 347-349
MSC (1991): Primary 17B67; Secondary 17B65
DOI: https://doi.org/10.1090/S0273-0979-96-00653-2
Review copyright: © Copyright 1996 American Mathematical Society
American Mathematical Society