The structures of ideals and subalgebras of free boundary lie superalgebras

ABSTRACT Ph. D. THESIS THE STRUCTURES OF IDEALS AND SUBALGEBRAS OF FREE BOUNDARY LD2 SUPERALGEBRAS Perihan DİNÇ (ARTUT) DEPARTMENT OF MATHEMATICS INSTITUTE OF NATURAL AND APPLIED SCIENCES UNIVERSITY OF ÇUKUROVA Supervisor: Prof. Dr. Melih BORAL Year: 1998, Pages: 35 Jury : Prof. Dr. Melih BORAL : Prof. Dr. Naime EKİCİ : Assist.Prof.Dr. Hasan DALGIN Let L = L- © Lj be a free Lie superalgebra on a finite set X = YuZ where Y and Z are disjoint. If Ln denotes the n-th term of the lower central series of L then Bn = L / Ln+i is the free nilpotent Lie superalgebra of class n on the generating set X. In this thesis, bases and dimensions of free nilpotent Lie superalgebra of class 5 are determined. In addition, some general results are obtained for free nilpotent Lie superalgebra for the special case Y = 0 and |Z| > 1. In the last chapter, it is proved that the only ideals which are free nilpotent subalgebras in a free nilpotent Lie superalgebra are free abelien or the whole algebra. Key Words : Nilpotent Algebra, Subalgebra, Ideal, Free Lie Algebra, Lie Supealgebra n