Iusa, Valentina, Mattarei, Sandro and Scarbolo, Claudio
(2021)
Graded Lie algebras of maximal class of type p.
Journal of Algebra, 588
.
pp. 77117.
ISSN 00218693
Full content URL: https://doi.org/10.1016/j.jalgebra.2021.08.013
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Abstract
The algebras of the title are infinitedimensional 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 VaughanLee in 2003. We announce an extension of that classification to arbitrary prime characteristic, and prove several major steps in its proof.
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