9 papers
Normal extensions of twisted graded Calabi--Yau algebras
Jason Gaddis, Dennis Keeler
We discuss three families of twisted graded Calabi--Yau algebras of dimension three that arise through the process of normal extensions. In addition to the twisted Calabi--Yau cond…
A family of algebras with trivial ozone group
Jason Gaddis, Daniel Yee
We study a family of Calabi--Yau algebras that include the quadratic Artin--Schelter regular algebras associated to a nodal cubic. It is shown that these algebras have trivial ozon…
Twisted generalized Weyl Poisson algebras of type
Jason Gaddis
We introduce a generalization of generalized Weyl Poisson algebras. This is a Poisson analogue of the twisted generalized Weyl algebras defined by Mazorchuk and Turowska. We prove…
Quiver down-up algebras of type A
Jason Gaddis, Dennis Keeler
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 quive…
Dimension two twisted graded Calabi--Yau algebras on two-vertex quivers
Jason Gaddis, Daryl Zazycki
We classify, up to isomorphism, twisted graded Calabi--Yau algebras of dimension two on two-vertex quivers. By work of Reyes and Rogalski, such algebras may be presented as quotien…
Log-ozone groups and centers of polynomial Poisson algebras
Kenneth Chan, Jason Gaddis, Robert Won +1
In previous work, the authors introduced the ozone group of an associative algebra as the subgroup of automorphisms which fix the center pointwise. The authors studied PI skew poly…