Cup product on Hochschild cohomology of a family of quiver algebras

2020/04/02 by Tolulope Oke, Oke, Tolulope
Mathematics · #13D03 (Secondary) #16E40 (Primary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2004.00780

openalex publication_date 2020/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Resolutions over Koszul algebras

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