Graded Lie algebras of maximal class of type p

The algebras of the title are infinite-dimensional graded Lie algebras L = circle plus L-infinity(i=1)i, over a field of positive characteristic p, which are generated by an element of degree 1and an element of degree p, and satisfy [L-i, L-1] = Li+1 for i >= p. In case p = 2 such algebras were classified by Caranti and VaughanLee in 2003. We announce an extension of that classification to arbitrary prime characteristic, and prove several major steps in its proof. (C) 2021 Elsevier Inc. All rights reserved.