The algebras of the title are infinite-dimensional graded Lie algebras L=⨁i=1∞Li, over a field of positive characteristic p, which are generated by an element of degree 1 and an element of degree p, ...and satisfy Li,L1=Li+1 for i≥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.
J. Algebra 588 (2021), 77-117 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 $i\ge p$. %of maximal class in the sense
that $L/L^i$ has dimension $i$ for all $i>1$. 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.
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 \(i\ge p\). %of maximal class in the sense that \(L/L^i\) has dimension \(i\) for all \(i>1\). 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.
Lie algebras of maximal class (or filiform Lie algebras) are the Lie-theoretic analogue of pro-p-groups of maximal class. In particular, they are 2-generated. If one further assumes that the algebras ...are graded over the positive integers, then over a field of characteristic p it has been shown that a classification is possible provided one generator has;
degree 1 and the other has either degree 1 or 2. In this thesis I give a classification of graded Lie algebras of maximal class with generators of degree 1 and p, respectively.
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