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Book Review
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Book Information
Author(s):
Victor G. Kac
Title:
Infinite dimensional Lie algebras
Additional book information:
second edition, Cambridge University Press, 1985, xvii + 280 pp., $24.95. ISBN 0-521-32133-6
References:
- 1.
- N. Bourbaki, Groupes et algèbres de Lie, Chaps. IV-VI, Paris, Hermann, 1968. MR 240238
- 2.
- I. B. Frenkel, J. Lepowsky and A. Meurman, A natural representation of the Fischer-Griess monster with the modular function J as character, Proc. Nat. Acad. Sci. U.S.A. 81 (1984), 3256-3260. MR 747596
- 3.
- O. Gabber and V. G. Kac, On defining relations of certain infinite-dimensional Lie algebras, Bull. Amer. Math. Soc. (N.S.) 5 (1981), 185-189. MR 621889
- 4.
- J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer, New York, 1972. MR 323842
- 5.
- N. Iwahori and H. Matsumoto, On some Bruhat decomposition and the structure of the Hecke rings of p-adic Chevalley groups, Publ. Math. Inst. Hautes Études Sci. 25 (1965), 5-48. MR 185016
- 6.
- I. L. Kantor, Graded Lie algebras, Trudy Sem. Vekt. Tens. Anal. 15 (1970), 227-266. (Russian) An English translation of an announcement of these results appeared in Soviet Math. Dokl. 9 (1968), 409-412. MR 297827
- 7.
- J. Lepowsky, Lie algebras and combinatorics, Proc. Internat. Congress of Mathematicians, Helsinki, 1978, pp. 579-584. MR 562658
- 8.
- J. Lepowsky and R. L. Wilson, A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities, Adv. in Math. 45 (1982), 21-72. MR 663415
- 9.
- J. Lepowsky and R. L. Wilson, The structure of standard modules. I. Universal algebras and the Rogers-Ramanujan identities. Invent. Math. 77 (1984), 199-290. MR 752821
- 10.
- J. Lepowsky and R. L. Wilson, The structure of standard modules. II. The case A, Invent. Math. 79 (1985), 417-442. MR 782227
- 11.
- R. V. Moody, Lie algebras associated with generalized Cartan matrices, Bull. Amer. Math. Soc. 73 (1967), 217-230. MR 207783
- 12.
- R. V. Moody, A new class of Lie algebras, J. Algebra 10 (1968), 211-230. MR 229687
- 13.
- R. V. Moody, Euclidean Lie algebras, Canad. J. Math. 21 (1969), 1432-1454. MR 255627
- 14.
- J.-P. Serre, Algèbres de Lie semi-simples complexes, Benjamin, New York and Amsterdam, 1966. MR 215886
- 15.
- I. Singer and S. Sternberg, On the infinite groups of Lie and Cartan, J. Analyse Math. 15 (1965), 1-114. MR 217822
- 16.
- G. M. Benkart, A Kac-Moody bibliography and some related references, Lie Algebras and Related Topics (D. J. Britten, F. W. Lemire, and R. V. Moody, eds.), Canadian Math. Soc. Conf. Proc. vol. 5, 1984, pp. 111-135, Amer. Math. Soc. Providence, R. I., 1986. MR 832196
- 17.
- I. B. Frenkel, Representations of affine Lie algebras, Hecke modular forms and KortewegdeVries type equations, Lie Algebras and Related Topics (D. J. Winter, ed.), Lecture Notes in Math., vol. 933, 1981, pp. 71-110. Springer-Verlag, Berlin-Heidelberg-New York, 1982. MR 675108
- 18.
- G. Segal and G. Wilson, Loop groups and equations of KdV type, Publ. Math. Inst. Hautes Études Sci. 61 (1985), 5-65. MR 783348
Additional Information:
Reviewer(s):
George B.
Seligman
Review Information:
Journal:
Bull. Amer. Math. Soc.
16
(1987),
144-149.
DOI:
10.1090/S0273-0979-1987-15492-9
PII:
S 0273-0979(1987)15492-9
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