Charlotte Scott Centre for Algebra

School of Mathematics & Physics, University of Lincoln

Paper accepted by Communications in Algebra

A paper by Sandro Mattarei, Constituents of graded Lie algebras of maximal class and chains of thin algebras, has been accepted for publication in Communications in Algebra. (See for a preprint version.)


Abstract: A thin Lie algebra is a Lie algebra L, graded over the positive integers, with its first homogeneous component L_1 of dimension two and generating L, and such that each nonzero ideal of L lies between consecutive terms of its lower central series. All homogeneous components of a thin Lie algebra have dimension one or two, and the two-dimensional components are called diamonds. If L_1 is the only diamond, then L is a graded Lie algebra of maximal class.

We present simpler proofs of some fundamental facts on graded Lie algebras of maximal class, and on thin Lie algebras, based on a uniform method, with emphasis on a polynomial interpretation. Among else, we determine the possible values for the most fundamental parameter of such algebras, which is one less than the dimension of their largest metabelian quotient.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.


This entry was posted on August 3, 2021 by in New publications, News and announcements, research.

Blog Stats

  • 29,290 hits


%d bloggers like this: