Higher Koszul algebras and the $\text{(Fg)}$-condition

Abstract

Determining when a finite dimensional algebra satisfies the finiteness property known as the $(\text{Fg})$-condition is of fundamental importance in the celebrated and influential theory of support varieties. We give an answer to this question for higher Koszul algebras, generalizing a result by Erdmann and Solberg. This allows us to establish a strong connection between the $(\text{Fg})$-condition and higher homological algebra, which significantly extends the classes of algebras for which it is known whether the $(\text{Fg})$-condition is satisfied. In particular, we show that the condition holds for an important class of algebras arising from consistent dimer models.

arXiv comment26 pages. Final version, accepted for publication in Ann. Represent. Theory