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
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
Departmental office: MC 5304
Phone: 519 888 4567 x43484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
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.