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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF   This review is available free of charge.
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?)

  • Jean-Pierre Serre, Algèbres de Lie semi-simples complexes, W. A. Benjamin, Inc., New York-Amsterdam, 1966 (French). MR 0215886
  • James E. Humphreys, Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, Vol. 9, Springer-Verlag, New York-Berlin, 1972. MR 0323842
  • Ofer Gabber and Victor G. Kac, On defining relations of certain infinite-dimensional Lie algebras, Bull. Amer. Math. Soc. (N.S.) 5 (1981), no. 2, 185–189. MR 621889, DOI 10.1090/S0273-0979-1981-14940-5
  • V. G. Kac, Simple irreducible graded Lie algebras of finite growth, Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968), 1323–1367 (Russian). MR 0259961
  • Robert V. Moody, A new class of Lie algebras, J. Algebra 10 (1968), 211–230. MR 229687, DOI 10.1016/0021-8693(68)90096-3
  • Victor G. Kac and Dale H. Peterson, Infinite-dimensional Lie algebras, theta functions and modular forms, Adv. in Math. 53 (1984), no. 2, 125–264. MR 750341, DOI 10.1016/0001-8708(84)90032-X
  • V. G. Kac and D. A. Kazhdan, Structure of representations with highest weight of infinite-dimensional Lie algebras, Adv. in Math. 34 (1979), no. 1, 97–108. MR 547842, DOI 10.1016/0001-8708(79)90066-5
  • I. N. Bernšteĭn, I. M. Gel′fand, and S. I. Gel′fand, Structure of representations that are generated by vectors of highest weight, Funckcional. Anal. i Priložen. 5 (1971), no. 1, 1–9 (Russian). MR 0291204
  • Victor G. Kac and Minoru Wakimoto, Modular invariant representations of infinite-dimensional Lie algebras and superalgebras, Proc. Nat. Acad. Sci. U.S.A. 85 (1988), no. 14, 4956–4960. MR 949675, DOI 10.1073/pnas.85.14.4956
  • Jacques Tits, Groupes associés aux algèbres de Kac-Moody, Astérisque 177-178 (1989), Exp. No. 700, 7–31 (French). Séminaire Bourbaki, Vol. 1988/89. MR 1040566
  • Victor G. Kac, Infinite-dimensional Lie algebras, 3rd ed., Cambridge University Press, Cambridge, 1990. MR 1104219, DOI 10.1017/CBO9780511626234

  • Review Information:

    Reviewer: George B. Seligman
    Affiliation: Yale University
    Journal: Bull. Amer. Math. Soc. 33 (1996), 347-349
    Review copyright: © Copyright 1996 American Mathematical Society