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

Emil Skoldberg

doi:10.1016/j.jpaa.2019.07.019

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

Emil Skoldberg

Mathematics

University of Galway

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

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 of these cohomology rings. (C) 2019 Elsevier B.V. All rights reserved.

Original language	English (Ireland)
Pages (from-to)	1320-1339
Number of pages	19
Journal	Journal Of Pure And Applied Algebra
Volume	224
Issue number	3
DOIs	https://doi.org/10.1016/j.jpaa.2019.07.019
Publication status	Published - 1 Mar 2020

Keywords

Hilbert series
Hochschild cohomology
Yoneda product

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Skoldberg, E;Tran, NTH

Access to Document

10.1016/j.jpaa.2019.07.019

Cite this

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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 of these cohomology rings. (C) 2019 Elsevier B.V. All rights reserved.",

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N2 - 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 of these cohomology rings. (C) 2019 Elsevier B.V. All rights reserved.

AB - 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 of these cohomology rings. (C) 2019 Elsevier B.V. All rights reserved.

KW - Hilbert series

KW - Hochschild cohomology

KW - Yoneda product

UR - https://www.scopus.com/pages/publications/85069667745

U2 - 10.1016/j.jpaa.2019.07.019

DO - 10.1016/j.jpaa.2019.07.019

M3 - Article

VL - 224

SP - 1320

EP - 1339

JO - Journal Of Pure And Applied Algebra

JF - Journal Of Pure And Applied Algebra

IS - 3

ER -

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

Abstract

Keywords

Authors (Note for portal: view the doc link for the full list of authors)

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