Transitivity and persistence properties of the subalgebras of a finite-dimensional Lie algebra

Author
Zahra Riyahi
University of Science and Technology of Mazandaran
Abstract
A subalgebra H of L is called an α -subalgebra, if H has the property α. Also, we say that a subalgebra H of a Lie algebra L is α -transitive, whenever each α -subalgebra of H is an α -subalgebra of L and a subalgebra H of L is α -sensitive if for every α -subalgebra K of H, there is an α -subalgebra A of L such that A⋂H=K . These concepts are analogous to the concepts of α -transitive and α -sensitive subgroups of finite groups. In this paper, the main results are based on the properties cover-avoidance, maximality, ideality, and c-ideality, and in particular, we examine α -transitive and maximal-sensitive subalgebras. Furthermore, we obtain the influence of these notions on the structure of finite-dimensional Lie algebras and we give some results about supersolvable Lie algebras.
Keywords
transitivity
sensitivity
Lie algebra
c -ideal
solvable
supersolvable
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