2020/12/04 by Clemens Koppensteiner, Koppensteiner, Clemens
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2012.02744
openalex publication_date 2020/12/04 · openalex created_date 2020/12/21 · openalex updated_date 2026/07/28
We discuss how the Hochschild cohomology of a dg category can be computed as the trace of its Serre functor. Applying this approach to the principal block of the Bernstein--Gelfand--Gelfand category O, we obtain its Hochschild cohomology as the compactly supported cohomology of an associated space. Equivalently, writing O as modules over the endomorphism algebra A of a minimal projective generator, this is the Hochschild cohomology of A. In particular our computation gives the Euler characteristic of the Hochschild cohomology of O in type A.