TY - JOUR
T1 - The Schreier technique for subalgebras of a free Lie aegebra
AU - Rosset, Shmuel
AU - Wasserman, Alon
PY - 1997/6
Y1 - 1997/6
N2 - In group theory Schreier's technique provides a basis for a subgroup of a tree group. In this paper an analogue is developed for free Lie algebras. It hinges on the idea of cutting a Hall set into two parts. Using it, we show that proper subalgebras of finite codimension are not finitely generated and, following M. Hall, that a finitely generated subalgebra is a free factor of a subalgebra of finite codimension.
AB - In group theory Schreier's technique provides a basis for a subgroup of a tree group. In this paper an analogue is developed for free Lie algebras. It hinges on the idea of cutting a Hall set into two parts. Using it, we show that proper subalgebras of finite codimension are not finitely generated and, following M. Hall, that a finitely generated subalgebra is a free factor of a subalgebra of finite codimension.
UR - http://www.scopus.com/inward/record.url?scp=0031519783&partnerID=8YFLogxK
U2 - 10.4153/CJM-1997-028-8
DO - 10.4153/CJM-1997-028-8
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:0031519783
SN - 0008-414X
VL - 49
SP - 600
EP - 616
JO - Canadian Journal of Mathematics
JF - Canadian Journal of Mathematics
IS - 3
ER -