Victor Petrogradsky
Ulianovsk University, Russia
Two kinds of growth for Lie algebras.
Abstract: We discuss two kinds of growth for linear algebras: a) the growth of finitely generated algebras and b) so called "codimension growth". These types of growth are discussed in case of Lie algebras.
a) For finitely generated Lie algebras we consider an hierarchy of intermediate growths between polynomial and exponent. The respective generating functions are analytic in the unit circle.
b) For countably generated Lie algebras we consider an hierarchy of intermediate growths between exponent and factorial. The respective exponential generating functions are entire functions of complex variables.
These types of growth are illustrated on the varieties of solvable Lie algebras, where the solubility length is fixed.