# Paper accepted by Communications in Algebra

A paper by Sandro Mattarei, *Constituents of graded Lie algebras of maximal class and chains of thin algebras*, has been accepted for publication in *Communications in Algebra*. (See https://arxiv.org/abs/2011.04110 for a preprint version.)

*Abstract*: A thin Lie algebra is a Lie algebra , graded over the positive integers, with its first homogeneous component of dimension two and generating , and such that each nonzero ideal of 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. If is the only diamond, then is a graded Lie algebra of maximal class.

We present simpler proofs of some fundamental facts on graded Lie algebras of maximal class, and on thin Lie algebras, based on a uniform method, with emphasis on a polynomial interpretation. Among else, we determine the possible values for the most fundamental parameter of such algebras, which is one less than the dimension of their largest metabelian quotient.

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