Classification of a type of graded Lie algebras of maximal class

Charlotte Scott Centre for Algebra

A collaboration across countries and over several years has taken place between Sandro Mattarei and two of his former PhD students, Claudio Scarbolo and Valentina Iusa, resulting in a preprint which was recently submitted for publication: “Graded Lie algebras of maximal class of type p“. Valentina was the first Algebra PhD student of the Charlotte Scott Algebra Centre and worked under the joint supervision of Sandro and Evgeny Khukhro.

The preprint concerns infinite-dimensional Lie algebras, over a field of prime characteristic p, which are graded over the positive integers and have maximal class in the sense that the kth Lie power of L has codimension k in L, for all k>1. The type p qualifier refers to the fact that the focus is on those generated by an element of degree p, together with an element of degree 1. (The actual natural definition…

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