Graded Lie algebras of maximal class of type $p$

Abstract

The algebras of the title are infinite-dimensional graded Lie algebras $L={⨁}_{i=1}^{\infty }{L}_i$, over a field of positive characteristic $p$, that 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.

Author Accepted Manuscript, 41 pages. arXiv admin note: text overlap with arXiv:1911.00970