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 algebras which respect the $\ZZ$-grading. We also show that generically the invariant rings of Taft actions on quantum generalized Weyl algebras are commutative Kleinian singularities.Comment: Main theorems restated to better illustrate primary findings. To appear in Journal of Algebr
AbstractWe consider actions of pointed Hopf algebras on general quantum polynomials and their invari...
We establish the Schur-Weyl type duality between double affine Hecke algebras and quantum toroidal s...
Abstract We examine actions of finite-dimensional pointed Hopf algebras on central si...
Let k be an algebraically closed field of characteristic zero. In joint work with J. Cuadra, we show...
We classify quantum analogues of actions of finite subgroups G of SL₂(k) on commutative polynomial r...
Actions of semisimple Hopf algebras H over an algebraically closed field of characteristic zero on c...
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Let $H$ be a Hopf algebra that is $\mathbb Z$-graded as an algebra. We provide sufficient conditions...
A quantum symmetric pair consists of a quantum group $\mathbf U$ and its coideal subalgebra ${\mathb...
We prove in full generality that the generalized quantum affine Schur-Weyl duality functor, introduc...
AbstractWe propose the following principle to study pointed Hopf algebras, or more generally, Hopf a...
We show that under certain conditions a finite dimensional graded pointed Hopf algebra is an image o...
Strongly Z-graded algebras or principal circle bundles and associated line bundles or invertible bim...
We show that the shuffle algebra associated to a doubled quiver (determined by 3-variable wheel cond...
AbstractWe consider actions of pointed Hopf algebras on general quantum polynomials and their invari...
We establish the Schur-Weyl type duality between double affine Hecke algebras and quantum toroidal s...
Abstract We examine actions of finite-dimensional pointed Hopf algebras on central si...
Let k be an algebraically closed field of characteristic zero. In joint work with J. Cuadra, we show...
We classify quantum analogues of actions of finite subgroups G of SL₂(k) on commutative polynomial r...
Actions of semisimple Hopf algebras H over an algebraically closed field of characteristic zero on c...
We introduce the concept of a universal quantum linear semigroupoid (UQSGd), which is a weak bialgeb...
We use semi-derived Ringel-Hall algebras of quivers with loops to realize the whole quantum Borcherd...
Let $H$ be a Hopf algebra that is $\mathbb Z$-graded as an algebra. We provide sufficient conditions...
A quantum symmetric pair consists of a quantum group $\mathbf U$ and its coideal subalgebra ${\mathb...
We prove in full generality that the generalized quantum affine Schur-Weyl duality functor, introduc...
AbstractWe propose the following principle to study pointed Hopf algebras, or more generally, Hopf a...
We show that under certain conditions a finite dimensional graded pointed Hopf algebra is an image o...
Strongly Z-graded algebras or principal circle bundles and associated line bundles or invertible bim...
We show that the shuffle algebra associated to a doubled quiver (determined by 3-variable wheel cond...
AbstractWe consider actions of pointed Hopf algebras on general quantum polynomials and their invari...
We establish the Schur-Weyl type duality between double affine Hecke algebras and quantum toroidal s...
Abstract We examine actions of finite-dimensional pointed Hopf algebras on central si...
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