This article is cited in 9 papers

On the Hilbert Series of Koszul Algebras

D. I. Piontkovskii

Central Economics and Mathematics Institute, RAS

Abstract: A family of examples is obtained which shows that, generally, it is impossible to decide for known Hilbert series of a qudratic algebra and its dual algebra whether or not this algebra has the Koszul property. The simplest example is given by two finitely generated algebras concentrated at the degrees not exceeding five; one of these algebras is monomial, while the other is not a Koszul algebra. This proves the conjecture of Positselskii [pos].

UDC: 517.55

Received: 28.10.1999

DOI: 10.4213/faa246

 English version: Functional Analysis and Its Applications, 2001, 35:2, 133–137

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