American Mathematical Society

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

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, Springer-Verlag, New York-Berlin, 1972. Graduate Texts in Mathematics, Vol. 9. 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 https://doi.org/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 https://doi.org/10.1016/0021-8693%2868%2990096-3
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 https://doi.org/10.1016/0001-8708%2884%2990032-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 https://doi.org/10.1016/0001-8708%2879%2990066-5
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 https://doi.org/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

Review Information:

Reviewer: George B. Seligman
Affiliation: Yale University
Email: selig@math.yale.edu