Hochschild cohomology of algebras of differential operators tangent to a hyperplane arrangement.

par Francisco Kordon (Universidad de Buenos Aires)

jeudi 15 mars 2018, 14:00 → 15:00 Europe/Paris

112 (bât. Braconnier)

An arrangement of hyperplanes is a finite set of hyperplanes in a vector space of finite dimension. Given a hyperplane arrangement A in a vector space V, the Lie algebra of derivations tangent to the arrangement Der A consist of the derivations of S, the coordinate ring of V, that preserve each of the hyperplanes of A. This Lie algebra is a very useful invariant of the arrangement, since it is closely related to the geometry and combinatorics of the arrangement and the topology of its complement. In this talk I will present the associative algebra of differential operators of A, which is the associative algebra generated by Der A and S inside the algebra of endomorphisms of S, and I will show the computation of its Hochschild cohomology in some particular cases.