no. 3
Higher Koszul algebras and the $\mathbf{(Fg)}$-condition
Haugland, Johanne1, 2 orcid ; Sandøy, Mads Hustad2 orcid
1Faculty of Mathematics, Ruhr-Universität Bochum, 44780 Bochum, Germany
2Department of mathematical sciences, NTNU, NO-7491 Trondheim, Norway
Annals of Representation Theory, Volume 3 (2026) no. 3, pp. 487-508

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

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DOI: 10.5802/art.48
Classification: 16E40, 16S37, 16W50, 16G20, 16G60, 18G80
Keywords: higher Koszul algebra, $\mathbf{(Fg)}$-condition, support varieties, higher homological algebra, trivial extension, preprojective algebra, $n$-representation infinite algebra, $n$-representation tame algebra, dimer algebra, dimer model, $A_\infty $-algebra

Haugland, Johanne  1 , 2 ; Sandøy, Mads Hustad  2

1 Faculty of Mathematics, Ruhr-Universität Bochum, 44780 Bochum, Germany
2 Department of mathematical sciences, NTNU, NO-7491 Trondheim, Norway
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Haugland, Johanne; Sandøy, Mads Hustad. Higher Koszul algebras and the $\mathbf{(Fg)}$-condition. Annals of Representation Theory, Volume 3 (2026) no. 3, pp. 487-508. doi: 10.5802/art.48
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