The Yoneda Algebra of a 𝒦₂Algebra Need not be Another 𝒦₂Algebra

Abstract

Abstract. The Yoneda algebra of a Koszul algebra or a D-Koszul algebra is Koszul. K2 algebras are a natural generalization of Koszul algebras, and one would hope that the Yoneda algebra of a K2 algebra would be another K2 algebra. We show that this is not necessarily the case by constructing a monomial K2 algebra for which the corresponding Yoneda algebra is not K2.

The Yoneda Algebra of a Graded Ore Extension

“…The study of K 2 algebras is attractive because the first two cohomological degrees of E(A) are seen in a suitable presentation of A: we have E 1 (A) ≃ A * 1 while E 2 (A) is roughly dual to the essential relations of A. The class of K 2 algebras has been further studied in [2] and [7].…”