Charlotte Scott Centre for Algebra

School of Mathematics & Physics, University of Lincoln

A paper by Sandro Mattarei and Simone Ugolini, Graded Lie algebras of maximal class of type n, has been published in Journal of Algebra. Simone was Sandro’s PhD student at the University of Trento (supervised jointly with Andrea Caranti), and the paper contains and completes some work done in Simone’s PhD thesis of 2010. It relates closely to another recent paper of Sandro’s with Valentina Iusa and Claudio Scarbolo, bearing the similar title Graded Lie algebras of maximal class of type p. Follow this link for the online version (free access until 13 January 2022), or https://arxiv.org/abs/1911.00970 for a preprint version.

Abstract: Let $n>1$ be an integer. The algebras of the title, which we abbreviate as algebras of type $n$, are infinite-dimensional graded Lie algebras $L= \bigoplus_{i=1}^{\infty}L_i,$ which are generated by an element of degree 1 and an element of degree $n$, and satisfy $[L_i,L_1]=L_{i+1}$ for $i\ge n$. Algebras of type 2 were classified by Caranti and Vaughan-Lee in 2000 over any field of odd characteristic. In this paper we lay the foundations for a classification of algebras of arbitrary type $n$, over fields of sufficiently large characteristic relative to $n$. Our main result describes precisely all possibilities for the first constituent length of an algebra of type $n$, which is a numerical invariant closely related to the dimension of its largest metabelian quotient.

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This entry was posted on November 25, 2021 by in New publications, News and announcements, research, students.