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Quadratic algebras with Ext algebras generated in two degrees

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arXiv
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Abstract

We show that there exist non-Koszul graded algebras that appear to be Koszul up to any given cohomological degree. For any integer m>2 we exhibit a non-commutative quadratic algebra for which the corresponding bigraded Yoneda algebra is generated in degrees (1,1) and (m,m+1). The algebra is therefore not Koszul but is m-Koszul (in the sense of Backelin). These examples answer a question of Green and Marcos.

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