# Traces, Schubert calculus, and Hochschild cohomology of category $\mathcal{O}$.

@article{Koppensteiner2020TracesSC, title={Traces, Schubert calculus, and Hochschild cohomology of category \$\mathcal\{O\}\$.}, author={Clemens Koppensteiner}, journal={arXiv: Representation Theory}, year={2020} }

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… Expand

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