On theta pair for a proper subalgebra

Authors

ALI REZA SALEMKAR
Sara Chehrazi
HAMID MOHAMMADZADEH

Abstract

For a proper subalgebra K of a finite dimensional Lie algebra L, a pair (A,B) of subalgebras of L is called a \theta-pair if L = \langle A,K\rangle, B is the largest ideal of L contained in A\cap K and for each proper subalgebra C/B of A/B which is an ideal of L/B, we have L\neq C+K. In this article, using this concept, we give some characterizations of solvability and supersolvability of a finite dimensional Lie algebra.

DOI

10.3906/mat-1112-43

Keywords

\theta-pair, Lie algebra, solvable, supersolvable

First Page

592

Last Page

597

Recommended Citation

SALEMKAR, A. R, Chehrazi, S, & MOHAMMADZADEH, H (2013). On theta pair for a proper subalgebra. Turkish Journal of Mathematics 37 (4): 592-597. https://doi.org/10.3906/mat-1112-43