# Charlotte Scott Centre for Algebra

School of Mathematics & Physics, University of Lincoln

# 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 $L$, graded over the positive integers, with its first homogeneous component $L_1$ 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. If $L_1$ is the only diamond, then $L$ 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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This entry was posted on August 3, 2021 by in New publications, News and announcements, research.