26 citations · 168 across the 36 of their papers we have counts for
17 papers · 1 filter
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…
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.…
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…
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 $…
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.…
Hopf coactions on commutative algebras generated by a quadratically independent comodule
Pavel Etingof, Debashish Goswami, Arnab Mandal +1
Let A be a commutative unital algebra over an algebraically closed field k of characteristic not equal to 2, whose generators form a finite-dimensional subspace V, with no nontrivi…
Actions of some pointed Hopf algebras on path algebras of quivers
Ryan Kinser, Chelsea Walton
We classify Hopf actions of Taft algebras T(n) on path algebras of quivers, in the setting where the quiver is loopless, finite, and Schurian. As a corollary, we see that every qui…