Mattarei, Sandro (2021) Constituents of graded Lie algebras of maximal class and chains of thin Lie algebras. Communications in Algebra . ISSN 00927872
Full content URL: https://doi.org/10.1080/00927872.2021.1967368
Documents 

PDF
Chain_lengths.pdf  Whole Document Restricted to Repository staff only until 1 September 2022. 328kB 
Item Type:  Article 

Item Status:  Live Archive 
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 twodimensional 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 
Repository Staff Only: item control page