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Detecting Koszulness and related homological properties from the algebra structure of Koszul homology
Concordia Univ, Irvine, CA 92612, USA.
Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA.
Univ Genoa, Dipartimento Matemat, Via Dodecaneso 35, I-16146 Genoa, Italy.
Northwest Missouri State Univ, Dept Math & Stat, Maryville, MO 64468 USA .
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2018 (English)In: Nagoya mathematical journal, ISSN 0027-7630, E-ISSN 2152-6842, Vol. 238, p. 47-85Article in journal (Refereed) Published
Abstract [en]

Let k be a field and R a standard graded k-algebra. We denote by H^R the homology algebra of the Koszul complex on a minimal set of generators of the irrelevant ideal of R. We discuss the relationship between the multiplicative structure of H^R and the property that R is a Koszul algebra. More generally, we work in the setting of local rings and we show that certain conditions on the multiplicative structure of Koszul homology imply strong homological properties, such as existence of certain Golod homomorphisms, leading to explicit computations of Poincaré series. As an application, we show that the Poincaré series of all finitely generated modules over a stretched Cohen-Macaulay local ring are rational, sharing a common denominator. 

Place, publisher, year, edition, pages
2018. Vol. 238, p. 47-85
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-64389DOI: 10.1017/nmj.2018.20ISI: 000529209500003Scopus ID: 2-s2.0-85084306405OAI: oai:DiVA.org:mdh-64389DiVA, id: diva2:1801337
Available from: 2023-09-29 Created: 2023-09-29 Last updated: 2023-11-15Bibliographically approved

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