2018/07/26 by Francisco Kordon, Kordon, Francisco, Mariano Suárez-Álvarez +1
Mathematics · #14N20 #16E40 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.1807.10372
openalex publication_date 2018/07/26 · openalex created_date 2018/08/03 · openalex updated_date 2026/07/28
Given a central arrangement of lines A in a 2-dimensional vector space V over a field of characteristic zero, we study the algebra \mathcal D(\mathcal A) of differential operators on V which are logarithmic along \mathcal A. Among other things we determine the Hochschild cohomology of \mathcal 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 \mathcal D(\mathcal A) and classify the algebras of that form up to isomorphism.