Preprojective algebra structure on skew-group algebras
Louis-Philippe Thibault

TL;DR
This paper investigates conditions under which skew-group algebras associated with finite subgroups of SL(n, k) can be given a higher preprojective algebra structure, showing that certain subgroup configurations prevent such grading structures.
Contribution
It establishes that skew-group algebras from subgroups conjugate to products of smaller SL groups cannot be Morita equivalent to higher preprojective algebras, and constructs explicit bound quivers for these algebras.
Findings
Skew-group algebras from certain subgroup configurations lack higher preprojective algebra grading.
Explicit bound quivers for higher preprojective algebras over Koszul algebras are constructed.
Preprojective algebras over higher representation-infinite Koszul algebras are derivation-quotient algebras with superpotential relations.
Abstract
We give a class of finite subgroups for which the skew-group algebra does not admit the grading structure of a higher preprojective algebra. Namely, we prove that if a finite group is conjugate to a finite subgroup of , for some , then the skew-group algebra is not Morita equivalent to a higher preprojective algebra. This is related to the preprojective algebra structure on the tensor product of two Koszul bimodule Calabi-Yau algebras. We prove that such an algebra cannot be endowed with a grading structure as required for a higher preprojective algebra. Moreover, we construct explicitly the bound quiver of the higher preprojective algebra over a finite-dimensional Koszul algebra of finite global dimension. We show in addition that preprojective algebras over higher…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
