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arXiv · 2606.11641

Singular Hochschild complex and Cartan matrix

Yu Wang·Xiaozhuan Liang
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Abstract

If A is a symmetric algebra, then Hochschild homology of the dg enhancement of the singularity category of A agrees with singular Hochschild homology of A. For a basic finite dimensional k algebra A, the Cartan matrix of A is symmetric if and only if the k dual of the mixed complex of the dg enhancement of its singularity category is isomorphic to its shift by -1. We provide two counterexamples to show that neither result holds for general Frobenius algebras.

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Yu Wang, Xiaozhuan Liang. 2026-06-10. Singular Hochschild complex and Cartan matrix. https://arxiv.org/abs/2606.11641

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