相关论文: Classification of actions of discrete Kac algebras…

Let $\mathfrak{C}$ be the smallest class of countable discrete groups with the following properties: (i) $\mathfrak{C}$ contains the trivial group, (ii) $\mathfrak{C}$ is closed under isomorphisms, countable increasing unions and extensions…

Actions of algebraic groups on DG categories provide a convenient, unifying framework in some parts of geometric representation theory, especially the representation theory of reductive Lie algebras. We extend this theory to loop groups and…

Let X=spec A be a normal affine variety over an algebraically closed field k of characteristic 0 endowed with an effective action of a torus T of dimension n. Let also D be a homogeneous locally nilpotent derivation on the normal affine…

We study actions of discrete groups on 2-categories. The motivating examples are actions on the 2-category of representations of finite tensor categories and their relation with the extension theory of tensor categories by groups.…

We introduce {\it covariant structures} $\left\{(\A,\k),(\a,\aa),\(\ha,\haa\)\right\}$ formed of a separable $C^*$-algebra $\A$, a measurable twisted action $(\a,\aa)$ of the second-countable locally compact group $\G$\,, a measurable…

Let $A$ be a not necessarily commutative monoid with zero such that projective $A$-acts are free. This paper shows that the algebraic K-groups of $A$ can be defined using the +-construction and the Q-construction. It is shown that these two…

We study the algebras of differential operators invariant with respect to the scalar slash actions of real Jacobi groups of arbitrary rank. These algebras are non-commutative and are generated by their elements of orders 2 and 3. We prove…

This survey paper presents the discrete group viewpoint on Kac-Moody groups. Over finite fields, the latter groups are finitely generated; they act on new buildings enjoying remarkable negative curvature properties. The study of these…

It is known that a finite group G can only act freely on affine n-space if K has positive characteristic p and G is a p-group. In that case the group action is "non-linear" and the ring of regular functions must be a trace-surjective…

The equivariant coarse index is well-understood and widely used for actions by discrete groups. We extend the definition of this index to general locally compact groups. We use a suitable notion of admissible modules over $C^*$-algebras of…

We study actions of connected algebraic groups on normal algebraic varieties, and show how to reduce them to actions of affine subgroups.

It is proved that the ring of invariants of the standard smooth completion of a Kac-Moody Lie algebra is functionally generated by two elements: the coefficient of the center and the Killing form.

We work out the constraints imposed by SL(2C) invariance for sphere topology and modular invariance for torus topology, on the discretized form of Liouville action in Polyakov's non local covariant form. These are sufficient to completely…

We provide a framework for studying concrete C*-algebras associated with algebraic actions of semigroups: Given such an action, we construct an inverse semigroup, and we introduce conditions for algebraic actions that characterize…

We discuss two simple but useful observations that allow the construction of modular forms from given ones using invariant theory. The first one deals with elliptic modular forms and their derivatives, and generalizes the Rankin-Cohen…

Any finite set of linear operators on an algebra $A$ yields an operator algebra $B$ and a module structure on A, whose endomorphism ring is isomorphic to a subring $A^B$ of certain invariant elements of $A$. We show that if $A$ is a…

Starting from any proper action of any locally compact quantum group on any discrete quantum space, we show that its equivariant representation theory yields a concrete unitary 2-category of finite type Hilbert bimodules over the discrete…

Automorphisms of finite order and real forms of "smooth" affine Kac-Moody algebras are studied, i.e. of 2-dimensional extensions of the algebra of smooth loops in a simple Lie algebra. It is shown that they can be parametrized by certain…

In this paper, we study partial actions of groups on $R$-algebras, where $R$ is a commutative ring. We describe the partial actions of groups on the indecomposable algebras with enveloping actions. Then we work on algebras that can be…

This is the second paper in a series on intrinsic Donaldson-Thomas theory, a framework for studying the enumerative geometry of general algebraic stacks. In this paper, we present the construction of Donaldson-Thomas invariants for general…