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Tensor products of n-complete algebras
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.ORCID iD: 0000-0001-7611-7668
2019 (English)In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 223, no 8, p. 3537-3553Article in journal (Refereed) Published
Abstract [en]

If A and B are n- and m-representation finite k-algebras, then their tensor product Lambda = A circle times(k) B is not in general (n + m)-representation finite. However, we prove that if A and B are acyclic and satisfy the weaker assumption of n- and m-completeness, then A is (n + m)-complete. This mirrors the fact that taking higher Auslander algebra does not preserve d-representation finiteness in general, but it does preserve d-completeness. As a corollary, we get the necessary condition for A to be (n + m)-representation finite which was found by Herschend and Iyama by using a certain twisted fractionally Calabi-Yau property.

Place, publisher, year, edition, pages
2019. Vol. 223, no 8, p. 3537-3553
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:uu:diva-382236DOI: 10.1016/j.jpaa.2018.11.016ISI: 000462422200019OAI: oai:DiVA.org:uu-382236DiVA, id: diva2:1316148
Available from: 2019-05-16 Created: 2019-05-16 Last updated: 2019-05-16Bibliographically approved

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Pasquali, Andrea

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