A Classification of some Quadratic Algebras

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Date

1998-07-02

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Virginia Tech

Abstract

In this paper, for a select group of quadratic algebras, we investigate restrictions necessary on the generators of the ideal for the resulting algebra to be Koszul. Techniques include the use of Gröbner bases and development of Koszul resolutions. When the quadratic algebra is Koszul, we provide the associated linear resolution of the field. When not Koszul, we describe the maps of the resolution up to the instance of nonlinearity.

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Keywords

Koszul algebra, quadratic algebra, monomial generators

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