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Good and bad Koszul algebras and their Hochschild homology
Stockholm University, Faculty of Science, Department of Mathematics. Stockholm University, Faculty of Science, Department of Mathematics. matematik.
2005 (English)In: Journal of Pure and Applied Algebra, ISSN ISSN 0022-4049, Vol. 201, no 1-3, 295-327 p.Article in journal (Refereed) Published
Abstract [en]

A systematic study of the homological behavior of finitely and linearly presented modules over Koszul algebras is started. In particular, it is shown that the generating series of the linear Betti numbers of these modules over some precise special Koszul algebras are rationally related to the generating series for the Betti numbers of all local commutative noetherian rings. It is also shown that there are very small commutative Koszul algebras (4 generators and 4,5 or 6 relations) which are bad in the sense that rational generating series for Betti numbers of linearly presented modules over them cannot be put on a common denominator. Finally, we do some explicit calculations that indicate that if a Koszul algebra is not a local complete intersection, then the generating series for its Hochschild (and also cyclic homology) is an irrational function. This supports the conjecture that the answer to our Question 1 on pp. 185-186 of Roos (Varna (1986) 173-189; Lectures Notes in Mathematics, vol. 1352, Springer, Berlin, 1988) is positive.

Place, publisher, year, edition, pages
2005. Vol. 201, no 1-3, 295-327 p.
Keyword [en]
Koszul algebra, Hochschild homology, cyclic homology, Betti numbers, generating series
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-13287DOI: doi:10.1016/j.jpaa.2004.12.021OAI: oai:DiVA.org:su-13287DiVA: diva2:179807
Available from: 2008-03-13 Created: 2008-03-13 Last updated: 2011-01-12Bibliographically approved

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