## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Wednesday, March 12, 2014 — 2:30 PM EDT

It is typically difficult to classify the irreducible representations of a given algebra A. A good first step is to try to find the primitive ideals i.e. the annihilators of the simple modules. Primitive ideals are prime (in the noncommutative sense) and if one is lucky, the primitive ideals will coincide with two other types of prime ideals: (i) the prime ideals which are locally closed in Zariski topology and (ii) the prime ideals P of A which are such that the centre of the ring of fractions of A/P is an algebraic extension of the ground field (these are called rational ideals). When these ideals coincide, the algebra A is said to satisfy the Dixmier-Moeglin equivalence.

I will outline the proof of the Dixmier-Moeglin equivalence for a well-behaved class of Ore extensions, relying on Cauchon’s Deleting Derivations algorithm. I will discuss the hope that, in some such Ore extensions, the prime ideals which are any given ”distance” from being primitive will coincide with the prime ideals which are the same ”distance” from being locally closed and with the prime ideals which are the same ”distance” from being rational.

Location

MC - Mathematics & Computer Building

5046

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.