Constituents of graded Lie algebras of maximal class and chains of thin Lie algebras

Mattarei, Sandro (2021) Constituents of graded Lie algebras of maximal class and chains of thin Lie algebras. Communications in Algebra . ISSN 0092-7872

Full content URL: https://doi.org/10.1080/00927872.2021.1967368

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Constituents of graded Lie algebras of maximal class and chains of thin Lie algebras
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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.

Keywords:modular Lie algebra, graded Lie algebra, Lie algebra of maximal class, thin Lie algebra
Subjects:G Mathematical and Computer Sciences > G110 Pure Mathematics
Divisions:College of Science > School of Mathematics and Physics
ID Code:46687
Deposited On:29 Sep 2021 10:04

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