Finiteness conditions on the Yoneda algebra of a monomial algebra

TL;DR

This paper characterizes finiteness properties of the Yoneda algebra of a monomial algebra using a graph called the CPS graph, providing an algorithmic way to verify properties like finite generation.

Contribution

It introduces the CPS graph for monomial algebras and establishes criteria linking graph properties to finiteness conditions of the Yoneda algebra, including a terminating algorithm.

Findings

Finiteness properties are characterized by the CPS graph.

Finite generation can be checked algorithmically.

Finiteness conditions relate to graph-theoretic properties.

Abstract

Let A be a connected graded noncommutative monomial algebra. We associate to A a finite graph \Gamma(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 \Gamma(A). We show these properties, notably finite generation, can be checked by means of a terminating algorithm.