Integrality of exponents of some abelian-by-nilpotent varieties of Lie algebras

Authors
Mischchekno, SP Regev, A Zaicev, M
Citation
Sp. Mischchekno et al., Integrality of exponents of some abelian-by-nilpotent varieties of Lie algebras, COMM ALGEB, 28(9), 2000, pp. 4105-4130
Citations number
16
Categorie Soggetti
Mathematics
Journal title
COMMUNICATIONS IN ALGEBRA
ISSN journal
00927872 → ACNP
Volume
28
Issue
9
Year of publication
2000
Pages
4105 - 4130
Database
ISI
SICI code
0092-7872(2000)28:9<4105:IOEOSA>2.0.ZU;2-C
Abstract
Following I. Volichenko we study varieties of Lie algebras over a field of characteristic zero, satisfying the identity [[x(1),x(2),x(3)],[x(4), x(5), x(6)]] = 0. We prove that; the exponential growth of any proper subvariety is a positive integer and any positive integer can be so realized.