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arXiv · 2004.00780

Cup product on Hochschild cohomology of a family of quiver algebras

Tolulope Oke
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Abstract

Let k be a field, q in k. We derive a cup product formula on the Hochschild cohomology ring of a family Lambda_q of quiver algebras. Using this formula, we determine a subalgebra of k[x,y] isomorphic to Hochschild cohomology modulo N, where N is the ideal generated by homogeneous nilpotent elements. We explicitly construct non-nilpotent Hochschild cocycles which cannot be generated by lower homological degree elements, thus disproving the Snashall-Solberg finite generation conjecture.

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Tolulope Oke. 2020-04-02. Cup product on Hochschild cohomology of a family of quiver algebras. https://arxiv.org/abs/2004.00780

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