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
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
- 1.
- Serre, J.-P., Algèbres de Lie semi-simples complexes, Benjamin, New York, 1966. MR 0215886
- 2.
- Humphreys, J. E., Introduction to Lie algebras and representation theory, Springer, New York, 1972. MR 0323842
- 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 0621889
- 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 0259961
- 5.
- Moody, R. V., A new class of Lie algebras, J. Algebra 10 (1968), 211--230. MR 0229687
- 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 0750341
- 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 0547842
- 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 0291204
- 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 0949675
- 10.
- Tits, J., Groupes associés aux algèbres de Kac-Moody. Séminaire Bourbaki, Nov. 1988, Astérisque 177-178 (1988--89), 7--31. MR 1040566
- 11.
- Kac, V. G., Infinite dimensional Lie algebras, 3rd. ed., Cambridge Univ. Press, Cambridge, 1990. MR 1104219
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
