Growth of two-step solvable Lie algebras
HTML articles powered by AMS MathViewer
- by Shigeru Kobayashi and Manabu Sanami PDF
- Proc. Amer. Math. Soc. 109 (1990), 859-863 Request permission
Abstract:
It is proved that every finitely generated infinite-dimensional twostep solvable Lie algebra has polynomially bounded growth. As a corollary, it is shown that the universal enveloping algebras of such Lie algebras are not Noetherian but of Krull domain.References
- Ralph K. Amayo and Ian Stewart, Finitely generated Lie algebras, J. London Math. Soc. (2) 5 (1972), 697–703. MR 323850, DOI 10.1112/jlms/s2-5.4.697
- Marc Chamarie, Anneaux de Krull non commutatifs, J. Algebra 72 (1981), no. 1, 210–222 (French). MR 634623, DOI 10.1016/0021-8693(81)90318-5
- B. Hartley, Locally nilpotent ideals of a Lie algebra, Proc. Cambridge Philos. Soc. 63 (1967), 257–272. MR 213402, DOI 10.1017/s0305004100041177
- Arun Vinayak Jategaonkar, Ore domains and free algebras, Bull. London Math. Soc. 1 (1969), 45–46. MR 238881, DOI 10.1112/blms/1.1.45
- V. G. Kac, Simple irreducible graded Lie algebras of finite growth, Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968), 1323–1367 (Russian). MR 0259961 S. Kobayashi, Filtered rings whose associated graded rings are Krull, Comm. Algebra (to appear).
- G. R. Krause and T. H. Lenagan, Growth of algebras and Gel′fand-Kirillov dimension, Research Notes in Mathematics, vol. 116, Pitman (Advanced Publishing Program), Boston, MA, 1985. MR 781129
- Martha K. Smith, Universal enveloping algebras with subexponential but not polynomially bounded growth, Proc. Amer. Math. Soc. 60 (1976), 22–24 (1977). MR 419534, DOI 10.1090/S0002-9939-1976-0419534-5
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 859-863
- MSC: Primary 17B30; Secondary 16P90, 16S30, 17B35
- DOI: https://doi.org/10.1090/S0002-9939-1990-1015681-5
- MathSciNet review: 1015681