Journals / Turkish Journal of Mathematics / 2013 / Cilt: 37 - Sayı: 4
On theta pair for a proper subalgebra
- Pages
- 592–597
- DOI
- —
Abstract
For a proper subalgebra K of a finite dimensional Lie algebra L, a pair (A,B) of subalgebras of L is called a q-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.
Özet
For a proper subalgebra K of a finite dimensional Lie algebra L, a pair (A,B) of subalgebras of L is called a q-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.