On theta pair for a proper subalgebra

Authors

ALI REZA SALEMKAR
Sara Chehrazi
HAMID MOHAMMADZADEH

DOI

10.3906/mat-1112-43

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.

Keywords

\theta-pair, Lie algebra, solvable, supersolvable

First Page

592

Last Page

597

Recommended Citation

SALEMKAR, ALI REZA; Chehrazi, Sara; and MOHAMMADZADEH, HAMID (2013) "On theta pair for a proper subalgebra," Turkish Journal of Mathematics: Vol. 37: No. 4, Article 6. https://doi.org/10.3906/mat-1112-43
Available at: https://journals.tubitak.gov.tr/math/vol37/iss4/6