Mattarei, Sandro and Ugolini, Simone (2021) Graded Lie algebras of maximal class of type n. Journal of Algebra . ISSN 00218693
Full content URL: https://doi.org/10.1016/j.jalgebra.2021.11.012
Documents 

PDF
Algebras_of_type_n_revised.pdf  Whole Document Restricted to Repository staff only until 17 November 2022. Available under License Creative Commons AttributionNonCommercialNoDerivatives 4.0 International. 397kB 
Item Type:  Article 

Item Status:  Live Archive 
Abstract
Let n>1 be an integer. The algebras of the title, which we abbreviate as algebras of type n, are infinitedimensional 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 VaughanLee 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 
Repository Staff Only: item control page