Seminar: Goldie rank quasipolynomials via lattice point enumeration

Speaker: Joanna Meinel (Max Planck Institute for Mathematics, Bonn)

2012.09.20 | Christine Dilling

Date Wed 15 Feb
Time 14:15 15:15
Location Aud. D3 (1531-215)

Abstract

In 1998, Musson and Van den Bergh gave a classification of primitive ideals (the annihilators of simple modules) for a class of algebras related to the Weyl algebra $k[x_1,...,x_n,\partial_1,...,\partial_n]$. Similar to the case of universal enveloping algebras of semisimple complex Lie algebras, it suffices to look only at some of the simple modules to get a description of all primitive ideals. For the Weyl algebra this description can be made explicit in terms of lattice points and polyhedrons, which we will illustrate by a small example.
Then we want to study the quotients of our algebra with respect to the primitive ideals: Using the geometrical picture and Ehrhart theory, we construct for each nice family of such quotients a quasipolynomial that gives the Goldie rank of each quotient.

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