Related papers: Comodules for some simple $\mathcal O$-forms of $\…

In this note we give an example of affine quotient $G/H$ where $G$ is an affine algebraic group over an algebraically closed field of characteristic 0 and $H$ is a unipotent subgroup not contained in the unipotent radical of $G$. Some…

It is well-known that the category of comodules over a flat Hopf algebroid is abelian but typically fails to have enough projectives, and more generally, the category of graded comodules over a graded flat Hopf algebroid is abelian but…

We consider algebras defined over a complete, local and noetherian ground ring. They are gentle algebras in case the ground ring is a field. The unbounded homotopy category of complexes of projective modules is considered. Complexes with…

Let G be the (special) affine group, semidirect product of SL_n and C^n. In this paper we study the representation theory of G and in particular the question of rationality for V/G where V is a generically free G-representation. We show…

We give a complete description of the category of smooth complex representations of the multiplicative group of a central simple algebra over a locally compact nonarchimedean local field. More precisely, for each inertial class in the…

This paper classifies the derivations of group algebras in terms of the generators and defining relations of the group. If $RG$ is a group ring, where $R$ is commutative and $S$ is a set of generators of $G$ then necessary and sufficient…

Let $M$ be a $G$-manifold and $\om$ a $G$-invariant exact $m$-form on $M$. We indicate when these data allow us to constract a cocycle on a group $G$ with values in the trivial $G$-module $\mathbb R$ and when this cocycle is nontrivial.

We describe a fully faithful embedding of the category of (reflexive) globular sets into the category of counital cosymmetric $R$-coalgebras when $R$ is an integral domain. This embedding is a lift of the usual functor of $R$-chains and the…

Algebraic structures such as monoids, groups, and categories can be formulated within a category using commutative diagrams. In many common categories these reduce to familiar cases. In particular, group objects in Grp are abelian groups,…

We study the stack M of cameral covers for a complex reductive group G, introduced by Donagi and Gaitsgory. We compute its rational cohomology ring. In the special case G=GL(n), M is the stack of spectral covers. We also compute the…

In this paper, we give a method for relating the generalized category $\mathcal{O}$ defined by the author and collaborators to explicit finitely presented algebras, and apply this to quiver varieties. This allows us to describe…

Among all affine, flat, finitely presented group schemes, we focus on those that are pure, this includes all groups which are extensions of a finite locally free group by a group with connected fibres. We prove that over an arbitrary base…

We study a certain family of finite-dimensional simple representations over quantum affine superalgebras associated to general linear Lie superalgebras, the so-called fundamental representations: the denominators of rational $R$-matrices…

The generalized quantum group $\mathcal{U}(\epsilon)$ of type $A$ is an affine analogue of quantum group associated to a general linear Lie superalgebra $\mathfrak{gl}_{M|N}$. We prove that there exists a unique $R$ matrix on tensor product…

Quantum principal bundles or principal comodule algebras are re-interpreted as principal bundles within a framework of Synthetic Noncommutative Differential Geometry. More specifically, the notion of a noncommutative principal bundle within…

Let $X={\rm Spec}\: B$ be a factorial affine variety defined over an algebraically closed field $k$ of characteristic zero with a nontrivial action of the additive group $G_a$ associated to a locally nilpotent derivation $\delta$ on $B$.…

We give an algebraic description of the structure of the analytic universal cover of a complex abelian variety which suffices to determine the structure up to isomorphism. More generally, we classify the models of theories of "universal…

In this article, we construct affine group schemes $GL(X)$ where $X$ is any object in the Verlinde category in characteristic $p$ and classify their irreducible representations. We begin by showing that for a simple object $X$ of…

We classify affine varieties with an action of a connected, reductive algebraic group such that the group is isomorphic to an open orbit in the variety. This is accomplished by associating a set of one-parameter subgroups of the group to…

We classify fully commutative elements in the affine Coxeter group of type $\tilde{A_{n}}$. We give a normal form for such elements, then we propose an application of this normal form: we lift these fully commutative elements to the affine…