26 citations · 168 across the 36 of their papers we have counts for
43 papers
Reflective centers of module categories and quantum K-matrices
Robert Laugwitz, Chelsea Walton, Milen Yakimov
Our work is motivated by obtaining solutions to the quantum reflection equation (qRE) by categorical methods. To start, given a braided monoidal category and $\mathca…
On non-counital Frobenius algebras
Amanda Hernandez, Chelsea Walton, Harshit Yadav
A Frobenius algebra is a finite-dimensional algebra which comes equipped with a coassociative, counital comultiplication map that is an -bimodule map. Here, we examine c…
Constructing non-semisimple modular categories with local modules
Robert Laugwitz, Chelsea Walton
We define the class of rigid Frobenius algebras in a (non-semisimple) modular category and prove that their categories of local modules are, again, modular. This generalizes previo…
Filtered Frobenius algebras in monoidal categories
Chelsea Walton, Harshit Yadav
We develop filtered-graded techniques for algebras in monoidal categories with the main goal of establishing a categorical version of Bongale's 1967 result: A filtered deformation…
Algebraic properties of face algebras
Fabio Calderón, Chelsea Walton
Prompted an inquiry of Manin on whether a coacting Hopf-type structure and an algebra that is coacted upon share algebraic properties, we study the particular case of b…
Constructing non-semisimple modular categories with relative monoidal centers
Robert Laugwitz, Chelsea Walton
This paper is a contribution to the construction of non-semisimple modular categories. We establish when Müger centralizers inside non-semisimple modular categories are also modula…
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…
Algebraic structures in group-theoretical fusion categories
Yiby Morales, Monique Müller, Julia Plavnik +3
It was shown by Ostrik (2003) and Natale (2017) that a collection of twisted group algebras in a pointed fusion category serve as explicit Morita equivalence class representatives…
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…
Tensor algebras in finite tensor categories
Pavel Etingof, Ryan Kinser, Chelsea Walton
This paper introduces methods for classifying actions of finite-dimensional Hopf algebras on path algebras of quivers, and more generally on tensor algebras where is s…
Braided commutative algebras over quantized enveloping algebras
Robert Laugwitz, Chelsea Walton
We produce braided commutative algebras in braided monoidal categories by generalizing Davydov's full center construction of commutative algebras in centers of monoidal categories.…
Noncommutative Knörrer periodicity and noncommutative Kleinian singularities
Andrew Conner, Ellen Kirkman, W. Frank Moore +1
We establish a version of Knörrer's Periodicity Theorem in the context of noncommutative invariant theory. Namely, let be a left noetherian AS-regular algebra, let be a nor…
An Invitation to Noncommutative Algebra
Chelsea Walton
This is a brief introduction to the world of Noncommutative Algebra aimed at advanced undergraduate and beginning graduate students.
Gelfand-Kirillov dimension of cosemisimple Hopf algebras
Alexandru Chirvasitu, Chelsea Walton, Xingting Wang
In this note, we compute the Gelfand-Kirillov dimension of cosemisimple Hopf algebras that arise as deformations of a linearly reductive algebraic group. Our work lies in a purely…
On the quadratic dual of the Fomin-Kirillov algebras
Chelsea Walton, James J. Zhang
We study ring-theoretic and homological properties of the quadratic dual (or Koszul dual) of the Fomin-Kirillov algebras ; these algebras are conne…
PBW deformations of quadratic monomial algebras
Zachary Cline, Andrew Estornell, Chelsea Walton +1
A result of Braverman and Gaitsgory from 1996 gives necessary and sufficient conditions for a filtered algebra to be a Poincaré-Birkhoff-Witt (PBW) deformation of a Koszul algebra.…
Poisson geometry and representations of PI 4-dimensional Sklyanin algebras
Chelsea Walton, Xingting Wang, Milen Yakimov
Take S to be a 4-dimensional Sklyanin (elliptic) algebra that is module-finite over its center Z; thus, S is PI. Our first result is the construction of a Poisson Z-order structure…
Poisson geometry of PI 3-dimensional Sklyanin algebras
Chelsea Walton, Xingting Wang, Milen Yakimov
We give the 3-dimensional Sklyanin algebras that are module-finite over their center the structure of a Poisson -order (in the sense of Brown-Gordon). We show that the i…
Cocycle deformations and Galois objects for semisimple Hopf algebras of dimension and
Adriana Mejía Castaño, Susan Montgomery, Sonia Natale +2
Let and be distinct prime numbers. We study the Galois objects and cocycle deformations of the noncommutative, noncocommutative, semisimple Hopf algebras of odd dimension $…
McKay Correspondence for semisimple Hopf actions on regular graded algebras, II
Kenneth Chan, Ellen Kirkman, Chelsea Walton +1
We continue our study of the McKay Correspondence for grading preserving actions of semisimple Hopf algebras H on (noncommutative) Artin-Schelter regular algebras A. Here, we estab…
McKay Correspondence for semisimple Hopf actions on regular graded algebras, I
Kenneth Chan, Ellen Kirkman, Chelsea Walton +1
In establishing a more general version of the McKay correspondence, we prove Auslander's theorem for actions of semisimple Hopf algebras H on noncommutative Artin-Schelter regular…
On quantum groups associated to a pair of preregular forms
Alexandru Chirvasitu, Chelsea Walton, Xingting Wang
We define the universal quantum group that preserves a pair of Hopf comodule maps, whose underlying vector space maps are preregular forms defined on dual vector spac…
Finite dimensional Hopf actions on algebraic quantizations
Pavel Etingof, Chelsea Walton
Let k be an algebraically closed field of characteristic zero. In joint work with J. Cuadra [arxiv.org/abs/1409.1644, arxiv.org/abs/1509.01165], we showed that a semisimple Hopf ac…
Finite dimensional Hopf actions on deformation quantizations
Pavel Etingof, Chelsea Walton
We study when a finite dimensional Hopf action on a quantum formal deformation A of a commutative domain A_0 (i.e., a deformation quantization) must factor through a group algebra.…