School Seminars and Colloquia

Quantum polynomials

School Seminar

by Ashish Gupta

Institution: The University of Melbourne
Date: Tue 4th November 2008
Time: 12:00 PM
Location: Russell Love Theatre, Richard Berry Blg, The Uni of Melb

Abstract: Quantum polynomials (in two variables X and Y) differ from
ordinary polynomials in that XY = YX is no longer valid, but is replaced by XY = cYX, where c may be a complex number. Quantum polynomials were already mentioned in H. Weyl's book: The theory of groups and quantum mechanics. More recently quantum polynomials have gained importance for their role in Mathematical physics and non-commutative geometry. One of the concepts worth studying is that of modules over these polynomials which are quite analogous to the familiar vector spaces(the module elements may be multiplied by polynomials as well as scalars). As modules over quantum polynomials are mostly infinite dimensional as vector spaces, the suitable concept of dimension here is the growth of the module which is recorded in the degree a special polynomial - the Hilbert-Samuel polynomial. This new type of dimension is known as the
Gelfand-Kirillov(GK) dimension.

For More Information: Paul Norbury