A hyperbolic GCM Lie algebra and the Fibonacci numbers
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- by Alex Jay Feingold
- Proc. Amer. Math. Soc. 80 (1980), 379-385
- DOI: https://doi.org/10.1090/S0002-9939-1980-0580988-6
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Abstract:
The Fibonacci numbers are found to be involved with the Weyl-Macdonald-Kac denominator formula for a certain rank 2 Generalized Cartan Matrix Lie algebra.References
- S. Berman and R. V. Moody, Lie algebra multiplicities, Proc. Amer. Math. Soc. 76 (1979), no. 2, 223–228. MR 537078, DOI 10.1090/S0002-9939-1979-0537078-X
- V. G. Kac, Simple irreducible graded Lie algebras of finite growth, Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968), 1323–1367 (Russian). MR 0259961
- V. G. Kac, Infinite-dimensional Lie algebras, and the Dedekind $\eta$-function, Funkcional. Anal. i Priložen. 8 (1974), no. 1, 77–78 (Russian). MR 0374210
- J. Lepowsky, Lie algebras and combinatorics, Proceedings of the International Congress of Mathematicians (Helsinki, 1978) Acad. Sci. Fennica, Helsinki, 1980, pp. 579–584. MR 562658
- J. Lepowsky, Generalized Verma modules, loop space cohomology and MacDonald-type identities, Ann. Sci. École Norm. Sup. (4) 12 (1979), no. 2, 169–234. MR 543216
- James Lepowsky and Robert V. Moody, Hyperbolic Lie algebras and quasiregular cusps on Hilbert modular surfaces, Math. Ann. 245 (1979), no. 1, 63–88. MR 552580, DOI 10.1007/BF01420431
- I. G. Macdonald, Affine root systems and Dedekind’s $\eta$-function, Invent. Math. 15 (1972), 91–143. MR 357528, DOI 10.1007/BF01418931
- 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
- Robert V. Moody, Euclidean Lie algebras, Canadian J. Math. 21 (1969), 1432–1454. MR 255627, DOI 10.4153/CJM-1969-158-2
- R. V. Moody, Macdonald identities and Euclidean Lie algebras, Proc. Amer. Math. Soc. 48 (1975), 43–52. MR 442048, DOI 10.1090/S0002-9939-1975-0442048-2
- Robert V. Moody, Root systems of hyperbolic type, Adv. in Math. 33 (1979), no. 2, 144–160. MR 544847, DOI 10.1016/S0001-8708(79)80003-1
Bibliographic Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 379-385
- MSC: Primary 17B65; Secondary 10A20, 10A45
- DOI: https://doi.org/10.1090/S0002-9939-1980-0580988-6
- MathSciNet review: 580988