Jan-Erik Roos: New results about Hilbert series of noncommutative algebras

Let A be a graded associative algebra finitely generated in degree 1 (to simplify) over a field k. We are interested in calculating its Hilbert series, which in the commutative case is a rational function, but is not so in the non-commutative case in general. The calculation of these Hilbert series is a first step towards an understanding of the algebraic properties of some of these A:s which in particular come up when studying the Lie algebra of homotopy groups of a simply-connected space X or the graded associated Lie algebra of the lower central series of a finitely generated group. An important element in these investigations is a slight extension of a result of Govorov and Backelin as well as a recent important addition due to Backelin to the computer algebra BERGMAN (Backelin et al). In some cases it is necessary to go further using the program me lie dim by Clas Löfwall. Most notions described here will be defined from the beginning and the first 10 minutes of the seminar will be like a pre seminar. The last part of the seminar will be a computer demonstration of how this works in practice.