# Generalized Koszul properties for augmented algebras

SPEAKER: Christopher Phan

TITLE: Generalized Koszul properties for augmented algebras

ABSTRACT Under certain conditions, a filtration on an augmented algebra A admits a related filtration on the Yoneda algebra E(A) := Ext_A(K, K). We show that there exists a bigraded algebra monomorphism from gr E(A) to E_Gr(gr A), where E_Gr(gr A) is the graded Yoneda algebra of gr A. This monomorphism can sometimes be applied in the case where A is connected graded to determine that A has the K_2 property recently introduced by Cassidy and Shelton.