Geodesic
The Hochschild cohomology of the algebra of differential operators tangent to a central arrangement of lines
Documenta mathematica, Tome 27 (2022), pp. 869-916.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Given a central arrangement of lines $\mathcal{A}$ in a $2$-dimensional vector space $V$ over a field of characteristic zero, we study the algebra $\mathscr{D}(\mathcal{A})$ of differential operators on $V$ which are logarithmic along $\mathcal{A}$. Among other things we determine the Hochschild cohomology of $\mathscr{D}(\mathcal{A})$ as a Gerstenhaber algebra, establish a connection between that cohomology and the de Rham cohomology of the complement $M(\mathcal{A})$ of the arrangement, determine the isomorphism group of $\mathscr{D}(\mathcal{A})$ and classify the algebras of that form up to isomorphism.
Classification : 16E40, 14N20
Keywords: hyperplane arrangements, algebra of differential operators, Hochschild cohomology 
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     title = {The {Hochschild} cohomology of the algebra of differential operators tangent to a central arrangement of lines},
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Kordon, Francisco; Suárez-Álvarez, Mariano. The Hochschild cohomology of the algebra of differential operators tangent to a central arrangement of lines. Documenta mathematica, Tome 27 (2022), pp. 869-916. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a44/