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On the cap product in Hochschild theory
[Submitted on 6 Aug 2019 (v1), last revised 18 Jun 2026 (this ve · 2026-06-19 · via math updates on arXiv.org

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Abstract:In this paper, we give an axiomatic characterization of the cap product in the Hochschild theory of associative unital algebras which are projective over a commutative unital ring. We also give an interpretation of the cap product with coefficients in the algebra via chain maps. We illustrate these results by computing the cap product for truncated polynomial algebras $k[x]/(x^N)$ and for polynomial algebras, where it is identified with the contraction of differential forms by polyvector fields.

Submission history

From: Marco Armenta [view email]
[v1] Tue, 6 Aug 2019 16:50:27 UTC (8 KB)
[v2] Thu, 18 Jun 2026 13:00:10 UTC (15 KB)