Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Growth of two-step solvable Lie algebras

Authors: Shigeru Kobayashi and Manabu Sanami
Journal: Proc. Amer. Math. Soc. 109 (1990), 859-863
MSC: Primary 17B30; Secondary 16P90, 16S30, 17B35
MathSciNet review: 1015681
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] R. K. Amayoand I. Stewart, Finitely generated Lie algebras, J. London Math. Soc. 5 (1972), 697-703. MR 0323850 (48:2205)
  • [2] M. Charmarie, Anneaux de Krull non commutatifs, J. Algebra 72 (1981), 210-222. MR 634623 (83c:16003)
  • [3] B. Hartley, Locally nilpotent ideals of a Lie algebra, Proc. Cambridge Philos. Soc. 63 (1967), 257-272. MR 0213402 (35:4266)
  • [4] A. V. Jategaonkar, Ore domains and free algebras, Bull. London Math. Soc. 1 (1969), 45-46. MR 0238881 (39:241)
  • [5] V. G. Kac, Simple irreducible graded Lie algebras of finite growth, Math. USSR--Izvestija, 2 (1968), 1271-1311. MR 0259961 (41:4590)
  • [6] S. Kobayashi, Filtered rings whose associated graded rings are Krull, Comm. Algebra (to appear).
  • [7] G. R. Krause and T. H. Lenagan, Growth of algebras and Gelfant-Kirillov dimension, Pitman, 1985. MR 781129 (86g:16001)
  • [8] M. K. Smith, Universal enveloping algebras with subexponential but not polynomially bounded growth, Proc. Amer. Math. Soc. 60 (1976), 22-24. MR 0419534 (54:7555)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 17B30, 16P90, 16S30, 17B35

Retrieve articles in all journals with MSC: 17B30, 16P90, 16S30, 17B35

Additional Information

PII: S 0002-9939(1990)1015681-5
Article copyright: © Copyright 1990 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia