Lie algebra multiplicities
HTML articles powered by AMS MathViewer
- by S. Berman and R. V. Moody PDF
- Proc. Amer. Math. Soc. 76 (1979), 223-228 Request permission
Abstract:
Exact formulas for root space multiplicities in Cartan matrix Lie algebras and their universal enveloping algebras are computed. We go on to determine the number of free generators of each degree of the radicals defining these algebras.References
- S. Berman, Isomorphisms and automorphisms of universal Heffalump Lie algebras, Proc. Amer. Math. Soc. 65 (1977), no. 1, 29–34. MR 486024, DOI 10.1090/S0002-9939-1977-0486024-4 N. Bourbaki, Lie groups and Lie algebras, Part 1, Chapters 1-3, Addison-Wesley, Reading, Mass., 1975.
- Howard Garland and James Lepowsky, Lie algebra homology and the Macdonald-Kac formulas, Invent. Math. 34 (1976), no. 1, 37–76. MR 414645, DOI 10.1007/BF01418970
- 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 —, Simple irreducible graded Lie algebras of finite growth, Math. USSR-Izv. 2 (1968), 1271-1311.
- J. Lepowsky, Macdonald-type identities, Advances in Math. 27 (1978), no. 3, 230–234. MR 554353, DOI 10.1016/0001-8708(78)90099-3
- 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, Root systems of hyperbolic type, Adv. in Math. 33 (1979), no. 2, 144–160. MR 544847, DOI 10.1016/S0001-8708(79)80003-1
- 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
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 76 (1979), 223-228
- MSC: Primary 17B65; Secondary 17B20, 17B35
- DOI: https://doi.org/10.1090/S0002-9939-1979-0537078-X
- MathSciNet review: 537078