TY - JOUR
T1 - Quotients of maximal class of thin Lie algebras. The odd characteristic case
AU - Caranti, A.
AU - Jurman, G.
PY - 1999
Y1 - 1999
N2 - Among thin graded Lie algebras, which are particular instances of Lie algebras of finite width, there are many interesting objects, such as the graded Lie algebra associated to the Nottingham group. Among the factors of a thin algebra with respect to the terms of the lower central series, there is a greatest factor which is of maximal class. In thin Lie algebras associated to groups, this factor is metabelian. In this paper we show that the same holds in general, provided the characteristic of the underlying field is odd. In another paper by the second author it is shown that this is not the case for characteristic two.
AB - Among thin graded Lie algebras, which are particular instances of Lie algebras of finite width, there are many interesting objects, such as the graded Lie algebra associated to the Nottingham group. Among the factors of a thin algebra with respect to the terms of the lower central series, there is a greatest factor which is of maximal class. In thin Lie algebras associated to groups, this factor is metabelian. In this paper we show that the same holds in general, provided the characteristic of the underlying field is odd. In another paper by the second author it is shown that this is not the case for characteristic two.
KW - Graded Lie algebras of maximal class
KW - Thin Lie algebras
UR - http://www.scopus.com/inward/record.url?scp=26044450036&partnerID=8YFLogxK
U2 - 10.1080/00927879908826789
DO - 10.1080/00927879908826789
M3 - Article
SN - 0092-7872
VL - 27
SP - 5741
EP - 5748
JO - Communications in Algebra
JF - Communications in Algebra
IS - 12
ER -