Graded Lie algebras of maximal class of type n

Mattarei, Sandro and Ugolini, Simone (2021) Graded Lie algebras of maximal class of type n. Journal of Algebra . ISSN 0021-8693

Full content URL: https://doi.org/10.1016/j.jalgebra.2021.11.012

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Graded Lie algebras of maximal class of type n
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Abstract

Let n>1 be an integer. The algebras of the title, which we abbreviate as algebras of type n, are infinite-dimensional graded Lie algebras (L= direct sum of L_i for i from 1 to infinity) which are generated by an element of degree 1 and an element of degree n, and satisfy [L_i,L_1]=L_{i+1} for i>=n. Algebras of type 2 were classified by Caranti and Vaughan-Lee in 2000 over any field of odd characteristic. In this paper we lay the foundations for a classification of algebras of arbitrary type n, over fields of sufficiently large characteristic relative to n. Our main result describes precisely all possibilities for the first constituent length of an algebra of type n, which is a numerical invariant closely related to the dimension of its largest metabelian quotient.

Keywords:Modular Lie algebra, graded Lie algebra, Lie algebra of maximal class
Subjects:G Mathematical and Computer Sciences > G110 Pure Mathematics
Divisions:College of Science > School of Mathematics and Physics
ID Code:47383
Deposited On:22 Nov 2021 11:04

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