Texas A&M
University, Department of
Mathematics, 216 Milner Hall, 4th of February 2009, 3:00-3:50
Groups and Dynamics Seminar
Types of growth for Lie algebras and groups
Victor Petrogradsky of Ulyanovsk State University, Russia
The aim of the talk is to discuss different types of growth for Lie algebras.
There are natural examples of finitely generated Lie algebras that have
growths between polynomial and exponential. We suggest an hierarchy of
types of intermediate growth,
which consists of a countable series of functions. In terms of these
functions we describe the growth of finitely generated solvable Lie
algebras that have a fixed solubility length q and which are free under
this condition. We obtain an application of this result to free
solvable groups. Namely, we describe an asymptotic behaviour of the
lower central series for these groups. Respective generating functions
play an important role. They are analytic in the unit circle and we
obtain an hierarchy of types of growth for these functions, too.