{
  "id": "2012.02744",
  "version": "v1",
  "published": "2020-12-04T17:49:47.000Z",
  "updated": "2020-12-04T17:49:47.000Z",
  "title": "Traces, Schubert calculus, and Hochschild cohomology of category $\\mathcal{O}$",
  "authors": [
    "Clemens Koppensteiner"
  ],
  "comment": "9 pages",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "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 $\\mathcal{O}$, we obtain its Hochschild cohomology as the compactly supported cohomology of an associated space. Equivalently, writing $\\mathcal{O}$ 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 $\\mathcal{O}$ in type A.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-04T17:49:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hochschild cohomology",
      "schubert calculus",
      "dg category",
      "bernstein-gelfand-gelfand category",
      "minimal projective generator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}