Verification of Some Properties of the C-nilpotent Multiplier in Lie Algebras

Abstract

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 ${\gamma _d}(L)$ and $L/{Z_{d - 1}}(L)$. Finally, we compare our results with the previously known result.