# Paper accepted by the Proceedings of the Edinburgh Mathematical Society

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.

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