22/04/2016, 15:00 — 16:00 — Room 6.2.38, Faculty of Sciences of the Universidade de Lisboa
Samuel Lopes, Universidade do Porto
Invariants and Hochschild cohomology of rings of differential operators in one variable
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.
See also
sem_ceafel_2016_handout.pdf
