Samuel Lopes
Universidade do Porto

Abstract: A polynomial h in the variable x determines the derivation h(d/dx) of the polynomial ring F[x], and together with the multiplication operator on this ring, it generates a noncommutative algebra A_h whose elements can be written as differential operators on h(d/dx) with coefficients in F[x]. I will talk about some features of this algebra related to invariants under groups of automorphisms, derivations and the structure of the Hochschild cohomology Lie algebra of A_h, both in prime and zero characteristics. I will then explain how the complete Hochschild cohomology can be determined using the twisted Calabi-Yau property relative to a suitable ’Nakayama' automorphism.
This is joint work with G. Benkart and M. Ondrus.