School of Mathematics & Physics, University of Lincoln
A paper by Sandro Mattarei, A sandwich in thin Lie algebras, has been accepted for publication in the Proceedings of the Edinburgh Mathematical Society. (See https://arxiv.org/abs/2102.12662 for a preprint version.)
Abstract: A thin Lie algebra is a Lie algebra L, graded over the positive integers, with its first homogeneous component of dimension two and generating L, and such that each nonzero ideal of L lies between consecutive terms of its lower central series. All homogeneous components of a thin Lie algebra have dimension one or two, and the two-dimensional components are called diamonds.
Suppose the second diamond of L (that is, the next diamond past ) occurs in degree k. We prove that if , then for some nonzero element y of . In characteristic not two this means y is a sandwich element of L. We discuss the relevance of this fact in connection with an important theorem of Premet on sandwich elements in modular Lie algebras.