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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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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?)

  • 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
    Email: selig@math.yale.edu
    Journal: Bull. Amer. Math. Soc. 33 (1996), 347-349
    DOI: https://doi.org/10.1090/S0273-0979-96-00653-2
    Review copyright: © Copyright 1996 American Mathematical Society