## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Wednesday, September 30, 2015 — 2:30 PM EDT

Jason Bell, Pure Mathematics, University of Waterloo

"The noncommutative Zariski Cancellation Problem"

The Zariski Cancellation problem asks whether a complex affine variety X with X x C isomorphic to affine (n+1)-space must be isomorphic to affine n-space. Algebraically, this is asking about whether one can find a finitely generated C-algebra A such that A[x] is a polynomial ring but A is not. In this setting, one can formulate a noncommutative version. In the noncommutative setting, the analogue of a polynomial ring is an Artin-Schelter regular algebra. Just as with varieties, one can associate a dimension to AS-regular algebras that behaves like Krull dimension. We prove that the cancellation problem has an affirmative answer in dimension at most two. This is joint with James Zhang.

MC 5403

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

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