Finiteness conditions on the Yoneda algebra of a monomial algebra

摘要

Let A be a connected graded noncommutative monomial algebra. We associate to A a finite graph Γ(A) called the CPS graph of A. Finiteness properties of the Yoneda algebra Ext_A(k, k) including Noetherianity, finite GK dimension, and finite generation are characterized in terms of Γ(A). We show that these properties, notably finite generation, can be checked by means of a terminating algorithm.