School of Mathematics & Physics, University of Lincoln
Congratulations to our PhD student Valentina Iusa on her first paper being accepted for publication in Monatshefte für Mathematik!
Valentina’s paper, which bears the title “On the nilpotency class of some Lie algebras with a Frobenius group of automorphisms,” provides examples to show that a certain plausible bound on the nilpotency class of Lie algebras as in the title cannot exist.
Abstract: We construct a family of nilpotent Lie algebras, where each Lie algebra admits a metacyclic Frobenius group of automorphisms such that the fixed-point subalgebra of the kernel is trivial and the fixed-point subalgebra of the complement is abelian. We prove that the nilpotency class of Lie algebras belonging to this family is unbounded. Specifically, for every natural number there exists a Lie algebra in with nilpotency class at least .