L. G. Kovács’ Work on Lie Powers

Abstract

From the mid-1990s onwards, the main focus of L. G. Kovács’ research was on Lie powers. This brief survey presents some of the key results on Lie powers obtained by Kovács and his collaborators, and discusses some subsequent developments and applications of this work.

Maximal linear groups induced on the Frattini quotient of a p-group

“…and let L(V ) be the closure of V under this bracket operation. Then L(V ) = n 1 L n V is a free Lie F-algebra by Witt's Theorem, where L n V := T n V ∩ L(V ) is called the n-th Lie power of V , see [4,20]. Note that…”

“…In this section, we consider the relevant Lie representation theory for our results. A good introduction to this topic is [20]. As noted in §2, the action of GL(V ) on V induces an action on the tensor algebra T (V ), and on L(V ) (which is a subset of T n V containing V , closed under the Lie bracket [ , ]).…”