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Séminaire Algèbre ICJ

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

## by Francisco Kordon (Universidad de Buenos Aires)

jeudi 15 mars 2018 de au (Europe/Paris)
at bât. Braconnier ( 112 )
ICJ, UCBL - La Doua
 Description 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.