15 citations · 105 across the 29 of their papers we have counts for
29 papers
Non-attacking rook placements on crossword grids
Joel Brewster Lewis, Robert Won
We introduce the notion of a non-attacking rook placement on a crossword grid. A crossword grid is a collection of white squares (which comprise across and down words) and black sq…
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…
Homological Integrals for Weak Hopf Algebras
Daniel Rogalski, Robert Won, James J. Zhang
We introduce the notion of a homological integral for an infinite-dimensional weak Hopf algebra and use the homological integral to prove several structure theorems. For example, w…
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…
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…
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…
Symmetries of algebras captured by actions of weak Hopf algebras
Fabio Calderón, Hongdi Huang, Elizabeth Wicks +1
In this paper, we present a generalization of well-established results regarding symmetries of -algebras, where is a field. Traditionally, for a -algebra ,…
Weighted homological regularities
Ellen Kirkman, Robert Won, James J. Zhang
Let be a noetherian connected graded algebra. We introduce and study homological invariants that are weighted sums of the homological and internal degrees of cochain complexes…
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…
Homological regularities and concavities
Ellen Kirkman, Robert Won, James J. Zhang
This paper concerns homological notions of regularity for noncommutative algebras. Properties of an algebra are reflected in the regularities of certain (complexes of) -modu…
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…
Degree bounds for Hopf actions on Artin-Schelter regular algebras
Ellen Kirkman, Robert Won, James J. Zhang
We study semisimple Hopf algebra actions on Artin-Schelter regular algebras and prove several upper bounds on the degrees of the minimal generators of the invariant subring, and on…
Universal quantum semigroupoids
Hongdi Huang, Chelsea Walton, Elizabeth Wicks +1
We introduce the concept of a universal quantum linear semigroupoid (UQSGd), which is a weak bialgebra that coacts on a (not necessarily connected) graded algebra universally w…
Improved bounds on sizes of generalized caps in
Michael Tait, Robert Won
An -general set in is a set of points such that any subset of size is in general position. A -general set is often called a capset. In this paper, we study the…
A proof of the Brown--Goodearl Conjecture for weak Hopf algebras
Daniel Rogalski, Robert Won, James J. Zhang
Let be a weak Hopf algebra that is a finitely generated module over its affine center. We show that has finite self-injective dimension and so the Brown--Goodearl Conjectur…
Algebraic structures in comodule categories over weak bialgebras
Chelsea Walton, Elizabeth Wicks, Robert Won
For a bialgebra coacting on a -algebra , a classical result states that is a right -comodule algebra if and only if is an algebra in the monoidal category…
Semisimple Reflection Hopf Algebras of Dimension Sixteen
Luigi Ferraro, Ellen Kirkman, W. Frank Moore +1
For each nontrivial semisimple Hopf algebra of dimension sixteen over , the smallest dimension inner-faithful representation of acting on a quadratic AS regular…
Simple -graded domains of Gelfand-Kirillov dimension two
Luigi Ferraro, Jason Gaddis, Robert Won
Let be an algebraically closed field and a -graded finitely generated simple -algebra which is a domain of Gelfand-Kirillov dimension 2. We show that the cat…
Three infinite families of reflection Hopf algebras
Luigi Ferraro, Ellen Kirkman, W. Frank Moore +1
Let be a semisimple Hopf algebra acting on an Artin-Schelter regular algebra , homogeneously, inner-faithfully, preserving the grading on , and so that is an -modu…
Sidon sets and 2-caps in
Yixuan Huang, Michael Tait, Robert Won
For each natural number , we introduce the concept of a -cap in . A subset of is called a -cap if, for each , no …
Fixed rings of generalized Weyl algebras
Jason Gaddis, Robert Won
We study actions by filtered automorphisms on classical generalized Weyl algebras (GWAs). In the case of a defining polynomial of degree two, we prove that the fixed ring under the…
Discriminants of Taft algebra smash products and applications
Jason Gaddis, Robert Won, Daniel Yee
A general criterion is given for when the center of a Taft algebra smash product is the fixed ring. This is applied to the study of the noncommutative discriminant. Our method reli…