标题： 高Koszul代数和$\textbf{(Fg)}$条件 显示英文标题

标题： Higher Koszul algebras and the $\textbf{(Fg)}$-condition

摘要： 确定一个有限维代数何时满足称为$(\textbf{Fg})$条件的有限性性质，在支持变体的著名且有影响力理论中具有基础重要性。 我们为更高Koszul代数回答了这个问题，推广了Erdmann和Solberg的一个结果。 这使我们能够建立$(\textbf{Fg})$条件与更高同调代数之间的强联系，这显著扩展了已知是否满足$(\textbf{Fg})$条件的代数类。 特别是，我们证明了该条件对于来自一致Dimer模型的重要代数类成立。 显示英文摘要

摘要： Determining when a finite dimensional algebra satisfies the finiteness property known as the $(\textbf{Fg})$-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 $(\textbf{Fg})$-condition and higher homological algebra, which significantly extends the classes of algebras for which it is known whether the $(\textbf{Fg})$-condition is satisfied. In particular, we show that the condition holds for an important class of algebras arising from consistent dimer models.