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Explicit Hochschild Cocycles for Gentle Algebras

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arxiv 2308.09533 v1 pith:HTGXW6MP submitted 2023-08-18 math.RA math.RT

Jasper van de Kreeke This is my paper · ORCID
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keywords hochschildalgebrascocyclescohomologyconstructionexplicitgentlepuncture
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Hochschild cohomology is crucial for understanding deformation theory. In arXiv:2304.10223, we have computed the Hochschild cohomology for gentle algebras of punctured surfaces. The construction of that paper is rather implicit and fails if the punctured surface has only a single puncture. In the present note, we supplement the earlier method by providing an explicit construction of Hochschild cocycles which also succeeds in the case of a single puncture.

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  1. $ L_\infty $-spectral sequences for Hochschild cohomology

    math.AT 2025-08 conditional novelty 6.0 of 10

    A new spectral-DGLA method preserves L-infinity structure through cohomology and re-proves formality for gentle algebras.

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