Algebra Seminar

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