Related papers: Taft algebra actions on preprojective algebras
We describe certain quiver Hopf algebras by parameters. This leads to the classification of multiple Taft algebras as well as pointed Yetter-Drinfeld modules and their corresponding Nichols algebras. In particular, when the ground-field $k$…
We lift the lattice of translations in the extended affine Weyl group to a braid group action on the quantum affine algebra. This action fixes the Heisenberg subalgebra pointwise. Loop like generators are found for the algebra which satisfy…
We first construct an action of the extended double affine braid group $\mathcal{\ddot{B}}$ on the quantum toroidal algebra $U_{q}(\mathfrak{g}_{\mathrm{tor}})$ in untwisted and twisted types. As a crucial step in the proof, we obtain a…
We define an integral form of shifted quantum affine algebras of type $A$ and construct Poincar\'e-Birkhoff-Witt-Drinfeld bases for them. When the shift is trivial, our integral form coincides with the RTT integral form. We prove that these…
This is the third in a series of papers which give an explicit description of the reconstruction algebra as a quiver with relations; these algebras arise naturally as geometric generalizations of preprojective algebras of extended Dynkin…
We consider a generalization of representations of quivers that can be derived from the ordinary representations of quivers by considering a product of arbitrary classical groups instead of a product of the general linear groups and by…
We study the invariant theory of a class of quantum Weyl algebras under group actions and prove that the fixed subrings are always Gorenstein. We also verify the Tits alternative for the automorphism groups of these quantum Weyl algebras.
We compute explicitly up to Morita-equivalence the skew group algebra of a finite group acting on the path algebra of a quiver and the skew group algebra of a finite group acting on a preprojective algebra. These results generalize previous…
Let $Q$ be a connected quiver with no oriented cycles, $k$ the field of complex numbers and $P$ a projective representation of $Q$. We study the adjoint action of the automorphism group $\Aut_{kQ} P$ on the space of radical endomorphisms…
Given a quiver, a fixed dimension vector, and a positive integer n, we construct a functor from the category of D-modules on the space of representations of the quiver to the category of modules over a corresponding Gan-Ginzburg algebra of…
We consider the quiver Yangians associated to general affine Dynkin diagrams. Although the quivers are generically not toric, the algebras have some similar structures. The odd reflections of the affine Dynkin diagrams should correspond to…
Given a graded ample Hausdorff groupoid, we realise its graded Steinberg algebra as a partial skew inverse semigroup ring. We use this to show that for a partial action of a discrete group on a locally compact Hausdorff topological space,…
We describe a method for an explicit determination of indecomposable preprojective and preinjective representations for extended Dynkin quivers by vector spaces and matrices. This method uses tilting theory and the explicit knowledge of…
We construct a collection of numerical invariants for approximately transitive (AT) actions (of $\Z$). We use them (sometimes supplemented by other invariants to show that members of various one-parameter families of AT actions are mutually…
We study actions of linear algebraic groups on central simple algebras using algebro-geometric techniques. Suppose an algebraic group G acts on a central simple algebra A of degree n. We are interested in questions of the following type:…
We define a projective variant of classical complex orientation theory. Using this, we construct a map of spectra which lifts the total Chern class, providing an alternative answer to an old question of Segal \cite{segal}, previously…
Given a partial action $\theta$ of a group on a set with an algebraic structure, we construct a reflector of $\theta$ in the corresponding subcategory of global actions and study the question when this reflector is a globalization. In…
In this paper, we study two-sided tilting complexes of preprojective algebras of Dynkin type. We construct the most fundamental class of two-sided tilting complexes, which has a group structure by derived tensor products and induces a group…
Our first collection of results parametrize (filtered) actions of a quantum Borel $U_q(\mathfrak{b}) \subset U_q(\mathfrak{sl}_2)$ on the path algebra of an arbitrary (finite) quiver. When $q$ is a root of unity, we give necessary and…
We will study two kinds of actions of a discrete amenable Kac algebra. The first one is an action whose modular part is normal. We will construct a new invariant which generalizes a characteristic invariant for a discrete group action, and…