26 citations · 168 across the 36 of their papers we have counts for
21 papers · 1 filter
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…
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…
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.…
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…
PBW deformations of braided products
Chelsea Walton, Sarah Witherspoon
We present new examples of deformations of smash product algebras that arise from Hopf algebra actions on pairs of module algebras. These examples involve module algebras that are…
Pointed Hopf actions on fields, II
Pavel Etingof, Chelsea Walton
This is a continuation of the authors' study of finite-dimensional pointed Hopf algebras H which act inner faithfully on commutative domains. As mentioned in Part I of this work, t…
Finite dimensional Hopf actions on Weyl algebras
Juan Cuadra, Pavel Etingof, Chelsea Walton
We prove that any action of a finite dimensional Hopf algebra H on a Weyl algebra A over an algebraically closed field of characteristic zero factors through a group action. In oth…
Maps from the enveloping algebra of the positive Witt algebra to regular algebras
Susan J. Sierra, Chelsea Walton
We construct homomorphisms from the universal enveloping algebra of the positive (part of the) Witt algebra to several different Artin-Schelter regular algebras, and determine thei…
On quantum groups associated to non-Noetherian regular algebras of dimension 2
Chelsea Walton, Xingting Wang
We investigate homological and ring-theoretic properties of universal quantum linear groups that coact on Artin-Schelter regular algebras A(n) of global dimension 2, especially wit…
Semisimple Hopf actions on Weyl algebras
Juan Cuadra, Pavel Etingof, Chelsea Walton
We study actions of semisimple Hopf algebras H on Weyl algebras A over a field of characteristic zero. We show that the action of H on A must factor through a group algebra; in oth…
Pointed Hopf actions on fields, I
Pavel Etingof, Chelsea Walton
Actions of semisimple Hopf algebras H over an algebraically closed field of characteristic zero on commutative domains were classified recently by the authors. The answer turns out…
Poincare-Birkhoff-Witt deformations of smash product algebras from Hopf actions on Koszul algebras
Chelsea Walton, Sarah Witherspoon
Let H be a Hopf algebra and let B be a Koszul H-module algebra. We provide necessary and sufficient conditions for a filtered algebra to be a Poincare-Birkhoff-Witt (PBW) deformati…
The universal enveloping algebra of the Witt algebra is not noetherian
Susan J. Sierra, Chelsea Walton
This work is prompted by the long standing question of whether it is possible for the universal enveloping algebra of an infinite dimensional Lie algebra to be noetherian. To addre…
Quantum binary polyhedral groups and their actions on quantum planes
Kenneth Chan, Ellen Kirkman, Chelsea Walton +1
We classify quantum analogues of actions of finite subgroups G of SL_2(k) on commutative polynomial rings k[u,v]. More precisely, we produce a classification of pairs (H,R), where…
Semisimple Hopf actions on commutative domains
Pavel Etingof, Chelsea Walton
Let H be a semisimple (so, finite dimensional) Hopf algebra over an algebraically closed field k of characteristic zero and let A be a commutative domain over k. We show that if A…
Hopf actions on filtered regular algebras
Kenneth Chan, Chelsea Walton, Yanhua Wang +1
We study finite dimensional Hopf algebra actions on so-called filtered Artin-Schelter regular algebras of dimension n, particularly on those of dimension 2. The first Weyl algebra…
Hopf actions and Nakayama automorphisms
Kenneth Chan, Chelsea Walton, James Zhang
Let H be a Hopf algebra with antipode S, and let A be an N-Koszul Artin-Schelter regular algebra. We study connections between the Nakayama automorphism of A and S^2 of H when H co…
Corrigendum to "Degenerate Sklyanin algebras and Generalized Twisted Homogeneous Coordinate rings", J. Algebra 322 (2009) 2508-2527
Chelsea M. Walton
There is an error in the computation of the truncated point schemes of the degenerate Sklyanin algebra S(1, 1, 1); they are larger than was claimed in Proposition 3.13 of the above…
Degenerate Sklyanin algebras and Generalized Twisted Homogeneous Coordinate rings
Chelsea Walton
In this work, we introduce the point parameter ring B, a generalized twisted homogeneous coordinate ring associated to a degenerate version of the three-dimensional Sklyanin algebr…