The
purpose of this paper is to obtain some inequalities and certain bounds for the
dimension of the c-nilpotent multiplier of finite dimensional nilpotent Lie
algebras and their factor Lie algebras. Also, we give an inequality for the
dimension of the c-nilpotent multiplier of L connected with dimension of the
Lie algebras γd (L) and L / Zd−1 (L) . Finally, we compare our results with the
previously known result.
All Lie algebras referred to in this article are (of finiteor infinite dimension) over a fixed field F and the square brackets [ , ]
denotes the Lie product. Let 0→R→F→L→0 be a free presentation of a Lie algebra
L, where F is a free Lie algebra.
This is analogous to the
definition of the Baer-invariant of a group with respect to the variety of
nilpotent groups of class at most c given by Baer [1-3] (for more information
on the Baer invariant of groups).
The purpose of this paper is
to obtain some inequalities for the dimension of the c-nilpotent multiplier of
finite dimensional nilpotent Lie algebras and their factor Lie algebras
(Corollary 2.3 and Corollary 2.5). Finally, we compare our results to upper
bound given.
No comments:
Post a Comment