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arXiv · 2606.25694

Preprojective algebras and generalisations: A short survey

Aaron Chan·Osamu Iyama·Rene Marczinzik
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Abstract

The preprojective algebra of a hereditary algebra $H$ can be defined as a certain orbit construction of the regular representation generated by the Auslander-Reiten translation. In this short survey, we will look at two important generalisations, namely, the contracted preprojective algebra and the total preprojective algebra. We will include several open problems and questions motivated by examples in the hope to stimulate future research on general orbit algebras of $H$-modules.

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Aaron Chan, Osamu Iyama, Rene Marczinzik. 2026-06-24. Preprojective algebras and generalisations: A short survey. https://arxiv.org/abs/2606.25694

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