23 citations · 177 across the 41 of their papers we have counts for
41 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…
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…
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…
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…
Higher rank Bell--Rogalski algebras
Jason Gaddis, Daniele Rosso, Robert Won
We generalize a construction of Bell and Rogalski to realize new examples of -graded simple rings. This construction also generalizes TGWAs of type . In addi…
Hopf actions on Poisson algebras
Awn Alqahtani, Jason Gaddis, Xingting Wang
We study finite-dimensional Hopf actions on Poisson algebras and explore the phenomenon of quantum rigidity in this context. Our main focus is on filtered (and especially quadratic…
Taft algebra actions on preprojective algebras
Jason Gaddis, Amrei Oswald
We classify actions of generalized Taft algebras on preprojective algebras of extended Dynkin quivers of type . This may be viewed as an extension of the problem of classifying…
Actions of Taft Algebras on Noetherian Down-Up Algebras
Simon Crawford, Jason Gaddis, Robert Won
We consider actions of Taft algebras on noetherian graded down-up algebras. We classify all such actions and determine properties of the corresponding invariant rings . We ide…
Twists of twisted generalized Weyl algebras
Jason Gaddis, Daniele Rosso
We study graded twisted tensor products and graded twists of twisted generalized Weyl algebras (TGWAs). We show that the class of TGWAs is closed under these operations assuming mi…
Ozone groups of Artin--Schelter regular algebras satisfying a polynomial identity
Kenneth Chan, Jason Gaddis, Robert Won +1
We study the ozone group of noetherian Artin--Schelter regular algebras satisfying a polynomial identity (or PI for short). The ozone group was shown in previous work by the author…
The Weyl algebra and its friends: a survey
Jason Gaddis
We survey several generalizations of the Weyl algebra including generalized Weyl algebras, twisted generalized Weyl algebras, quantized Weyl algebras, and Bell-Rogalski algebras. A…
Four-vertex quivers supporting twisted graded Calabi-Yau algebras
Jason Gaddis, Thomas Lamkin, Thy Nguyen +1
We study quivers supporting twisted graded Calabi-Yau algebras, building on work of Rogalski and the first author. Specifically, we classify quivers on four vertices in which the N…
Ozone groups and centers of skew polynomial rings
Kenneth Chan, Jason Gaddis, Robert Won +1
We introduce the ozone group of a noncommutative algebra , defined as the group of automorphisms of which fix every element of its center. In order to initiate the study of…
Centers and automorphisms of PI Quantum Matrix Algebras
Jason Gaddis, Thomas Lamkin
We study PI quantum matrix algebras and their automorphisms using the noncommutative discriminant. In the multi-parameter case at and , we show that all automorphisms ar…
Weight modules over Bell--Rogalski algebras
Jason Gaddis, Daniele Rosso, Robert Won
We study a class of -graded algebras introduced by Bell and Rogalski. Their construction generalizes in large part that of rank one generalized Weyl algebras (GWAs). We…
Cancellation and skew cancellation for Poisson algebras
Jason Gaddis, Xingting Wang, Daniel Yee
We study the Zariski cancellation problem for Poisson algebras in three variables. In particular, we prove those with Poisson bracket either being quadratic or derived from a Lie a…
Auslander's Theorem for dihedral actions on preprojective algebras of type A
Jacob Barahona Kamsvaag, Jason Gaddis
Given an algebra and a finite group of automorphisms of , there is a natural map , called the Auslander map. A theorem of Auslande…
Reflexive hull discriminants and applications
Kenneth Chan, Jason Gaddis, Robert Won +1
We introduce the reflexive hull discriminant as a tool to study noncommutative algebras that are finitely generated, but not necessarily free, over their centers. As an example, we…
Pointed Hopf actions on quantum generalized Weyl algebras
Jason Gaddis, Robert Won
We study actions of pointed Hopf algebras in the $\ZZ$-graded setting. Our main result classifies inner-faithful actions of generalized Taft algebras on quantum generalized Weyl al…
Fixed rings of twisted generalized Weyl algebras
Jason Gaddis, Daniele Rosso
Twisted generalized Weyl algebras (TGWAs) are a large family of algebras that includes several algebras of interest for ring theory and representation theory, such as Weyl algebras…
Reflection Groups and Rigidity of Quadratic Poisson Algebras
Jason Gaddis, Padmini Veerapen, Xingting Wang
In this paper, we study the invariant theory of quadratic Poisson algebras. Let G be a finite group of the graded Poisson automorphisms of a quadratic Poisson algebra A. When the P…
Fixed rings of quantum generalized Weyl algebras
Jason Gaddis, Phuong Ho
Generalized Weyl Algebras (GWAs) appear in diverse areas of mathematics including mathematical physics, noncommutative algebra, and representation theory. We study the invariants o…