Growth of subalgebras and subideals in free Lie algebras

JOURNAL OF ALGEBRA

卷:422

Article

Bahturin, Yuri¹  Olshanskii, Alexander^2,3 

[1] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada

[2] Vanderbilt Univ, Dept Math, Stevenson Ctr 1326, Nashville, TN 37240 USA

[3] Moscow MV Lomonosov State Univ, Fac Mech & Math, Dept Algebra, Moscow 119991, Russia

关键词: Free Lie algebras;    Free associative algebras;    Growth functions;   

DOI  :  10.1016/j.jalgebra.2014.07.039

来源: Elsevier

【 摘 要 】

We investigate subalgebras in free Lie algebras, the main tool being relative growth and cogrowth functions. Our study reveals drastic differences in the behavior of proper finitely generated subalgebras and nonzero subideals. For instance, the growth of a proper finitely generated subalgebra H of a free Lie algebra L, with respect to any fixed free basis X, is exponentially small compared to the growth of the whole of L. Quite opposite, the cogrowth of any nonzero subideal S is exponentially small compared to the growth of L. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free