URegina Topology & Geometry Seminar: Allen Herman

If A is an algebra over a field k, and R is an augmented commutative k-algebra, then an R-deformation of A is (intuitively) an R-algebra B whose underlying k-algebra structure is isomorphic to that of A. Two R-deformations of A are considered equivalent when there is an R-algebra isomorphism between the two that reduces to the expected isomorphism of their underlying k-algebra structures. In this talk we will see that in the cases R = k[[t]] (formal deformations) and R=k[t]/(t^2) (infinitesimal deformations), the equivalence classes of R-deformations of A can be understood using tools from Hochschild cohomology.