# Graded Lie algebras of maximal class of type p

Iusa, Valentina, Mattarei, Sandro and Scarbolo, Claudio (2021) Graded Lie algebras of maximal class of type p. Journal of Algebra, 588 . pp. 77-117. ISSN 0021-8693

Full content URL: https://doi.org/10.1016/j.jalgebra.2021.08.013

 Documents
 Graded Lie algebras of maximal class of type p Authors' Accepted Manuscript Format: PDFRepository staff only until 26 August 2022Size: 475kB
 PDF IMS.pdf - Whole Document Restricted to Repository staff only until 26 August 2022. 475kB
Item Type: Article Live Archive

## Abstract

The algebras of the title are infinite-dimensional graded Lie algebras $L= \bigoplus_{i=1}^{\infty}L_i$, over a field of positive characteristic $p$, which are generated by an element of degree $1$ and an element of degree $p$, and satisfy
$[L_i,L_1]=L_{i+1}$ for $i\ge p$. In case $p=2$ such algebras were classified by Caranti and Vaughan-Lee in 2003. We announce an extension of that classification to arbitrary prime characteristic, and prove several major steps in its proof.

Keywords: modular Lie algebra, graded Lie algebra, Lie algebra of maximal class G Mathematical and Computer Sciences > G110 Pure Mathematics College of Science > School of Mathematics and Physics 46691 06 Oct 2021 09:25

Repository Staff Only: item control page