Relation between the Hilbert series of quadratic dual algebras does not imply the Koszul property (Q1916680)
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scientific article; zbMATH DE number 898984
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Relation between the Hilbert series of quadratic dual algebras does not imply the Koszul property |
scientific article; zbMATH DE number 898984 |
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Relation between the Hilbert series of quadratic dual algebras does not imply the Koszul property (English)
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14 October 1996
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Let \(A\) be a quadratic algebra. The author shows that Fröberg's formula does not imply in general that \(A\) is a Koszul algebra. The counterexample is realized as a Segre tensor product. It is also shown that the double Poincaré series \(P_A(s,t)\) does not determine the Poincaré series \(P_{A^!}(s,t)\) of the dual algebra \(A^!\).
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quadratic algebras
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Fröberg's formula
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Koszul algebras
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Segre tensor products
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double Poincaré series
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dual algebras
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