Quiver down-up algebras

2025/12/02 by Gaddis, Jason, Keeler, Dennis
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2512.02821

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. The \NN-graded members of the family are proved to be, generically, twisted Calabi--Yau. Finally, we consider the isomorphism problem for graded quiver down-up algebras.

Citations

• Dimension two twisted graded Calabi--Yau algebras on two-vertex quivers
• Superpotentials and Quiver Algebras for Semisimple Hopf Actions
• Skew Calabi-Yau property of normal extensions
• Invariant Theory of Finite Group Actions on Down-Up Algebras
• Superpotentials and Higher Order Derivations
• Poincare-Birkhoff-Witt Deformations of Calabi-Yau Algebras

Related

• Dimension two twisted graded Calabi--Yau algebras on two-vertex quivers
• Classification of silted algebras for two quivers of Dynkin type \mathbbD_n
• Generalized quiver varieties and triangulated categories
• Quivers, desingularizations and canonical bases
• Graded quiver varieties and derived categories