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Infinite Dimensional Lie Algebras of Type L

2003; Taylor & Francis; Volume: 31; Issue: 5 Linguagem: Inglês

10.1081/agb-120019006

1532-4125

J. Marshall Osborn, Kaiming Zhao,

Finite Group Theory Research

Abstract In this paper, a class of infinite dimensional Lie algebras L(A, δ, α) over a field of characteristic 0 are studied. These Lie algebras, which we call here Lie algebras of type L, arose as one subclass in the recent classification of generalized Block algebras. We exhibit a large subclass of these algebras which are simple, as well as another subclass of these algebras which are never simple. For n > 1, simple Lie algebras of type L do not occur in any other known class of simple Lie algebras. In particular, for n > 1, these algebras have no toral elements. Simplicity in these algebras is equivalent to simplicity of an appropriate subalgebra. The notion of transitive ideal plays an important role in this theory.