Abstract
Simple toral rank 1 Lie algebras have been classified in Wilson [8]. This paper is concerned with the structure of a nonsimple toral rank 1 Lie algebra with respect to a specified "toral rank 1" Cartan subalgebra or, equivalently, with the structure of a nonsimple graded Lie algebra where the grading is the cyclic group grading determined by a specific "toral rank 1" Cartan subalgebra. Such graded Lie algebras are called cyclic Lie algebras, to distinguish them from ungraded toral rank 1 Lie algebras and from graded toral rank 1 Lie algebras where the grading is not a cyclic group grading determined by a "toral rank 1" Cartan subalgebra. The structure theorems on cyclic Lie algebras of this paper are established by studying L L in terms of its graded subalgebras and quotient algebras. Their importance is due to the central role which cyclic Lie algebras play in the theory of Lie algebra rootsystems.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have