The Yoneda algebra of a K_2 algebra need not be another K_2 algebra

TL;DR

This paper demonstrates that the Yoneda algebra of a K_2 algebra does not always retain the K_2 property, challenging assumptions about their structural preservation.

Contribution

It provides a counterexample showing that the Yoneda algebra of a K_2 algebra need not be K_2, unlike Koszul algebras.

Findings

Constructed a monomial K_2 algebra with a non-K_2 Yoneda algebra

Challenged the expectation that Yoneda algebras of K_2 algebras are always K_2

Provided insights into the limitations of K_2 algebra properties

Abstract

The Yoneda algebra of a Koszul algebra or a D-Koszul algebra is Koszul. K_2 algebras are a natural generalization of Koszul algebras, and one would hope that the Yoneda algebra of a K_2 algebra would be another K_2 algebra. We show that this is not necessarily the case by constructing a monomial K_2 algebra for which the corresponding Yoneda algebra is not K_2.