The Hochschild cohomology ring of the numerical semigroup algebras of embedding dimension two

2019/04/11 by Nghia T. H. Tran, Tran, Nghia T. H., Emil Sköldberg +1
Mathematics · #13D03 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1904.05733

openalex publication_date 2019/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let a and b be two coprime positive integers and k an arbitrary field. We determine the ring structure of the Hochschild cohomology of the numerical semigroup algebras k[s^a,s^b] of embedding dimension two (thus also complete intersections) in terms of generators and relations. In addition, we compute the Hilbert series for this cohomology ring.

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