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arXiv · 2512.02821

Quiver down-up algebras of type A

Jason Gaddis·Dennis Keeler
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Abstract

We present a generalization of down-up algebras, originally defined by Benkart and Roby. These quiver down-up algebras arise as quotients of the double of the extended Dynkin quiver of type A. Under a certain non-degeneracy condition, we show that quiver down-up algebras are noetherian piecewise domains, and that they are twisted Calabi--Yau. Finally, we consider the isomorphism problem for graded quiver down-up algebras.

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Jason Gaddis, Dennis Keeler. 2025-12-02. Quiver down-up algebras of type A. https://arxiv.org/abs/2512.02821

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