Related papers: Simplicial $*$-modules and mild actions

We introduce a notion of ellipticity of complexes of linear pseudodifferential operators acting on sections of $A$-Hilbert bundles over smooth manifolds, $A$ being a $C^*$-algebra. We prove that the cohomology groups of an $A$-elliptic…

Let $G$ be a semisimple Lie group with finite component group, and let $K<G$ be a maximal compact subgroup. We obtain a quantisation commutes with reduction result for actions by $G$ on manifolds of the form $M = G\times_K N$, where $N$ is…

This paper is, essentially, a survey related to the problem of understanding the combinatorics of the action of the monoidal category of finite dimensional modules over a simple finite dimensional Lie algebra on various categories of Lie…

Group actions on a Smale space and the actions induced on the C*-algebras associated to such a dynamical system are studied. We show that an effective action of a discrete group on a mixing Smale space produces a strongly outer action on…

Given a full right-Hilbert C*-module $\mathbf{X}$ over a C*-algebra $A$, the set $\mathbb{K}_{A}(\mathbf{X})$ of $A$-compact operators on $\mathbf{X}$ is the (up to isomorphism) unique C*-algebra that is strongly Morita equivalent to the…

In this paper, we introduce the notion of invariant submodule in the theory of Hilbert C*-modules and study some basic properties of bounded adjointable operators and their generalized inverses which have nontrivial invariant submodules. We…

Simple-minded systems in stable module categories are defined by orthogonality and generating properties so that the images of the simple modules under a stable equivalence form such a system. Simple-minded systems are shown to be invariant…

Taking advantage of the quantale-theoretic description of \'etale groupoids we study principal bundles, Hilsum-Skandalis maps, and Morita equivalence in terms of modules on inverse quantal frames. The Hilbert module description of quantale…

Building on structure observed in equivariant homotopy theory, we define an equivariant generalization of a symmetric monoidal category: a $G$-symmetric monoidal category. These record not only the symmetric monoidal products but also…

We determine the action of the product of symmetric groups on the cohomology of certain moduli of weighted pointed rational curves. The moduli spaces that we study are of stable rational curves with m+n marked points where the first m…

We associate a non-commutative $C^*$-algebra with any locally finite simplicial complex. We determine the $K$-theory of these algebras and show that they can be used to obtain a conceptual explanation for the Baum-Connes conjecture.

The notion of qausi-product actions of a compact group on a C$^*$-algebra was introduced by Bratteli et al. in their attempt to seek an equivariant analogue of Glimm's characterization of non-type I C$^*$-algebras. We show that a faithful…

Consider the polynomial ring in countably infinitely many variables over a field of characteristic zero, together with its natural action of the infinite general linear group G. We study the algebraic and homological properties of finitely…

We develop the foundations of $G$-global homotopy theory as a synthesis of classical equivariant homotopy theory on the one hand and global homotopy theory in the sense of Schwede on the other hand. Using this framework, we then introduce…

Let G be a finite group acting linearly on the polynomial ring with invariant ring R. If the action is small, then a classical result of Auslander gives in dimension two a correspondence between linear representations of G and maximal…

The stable category of modules over the algebra of a finite group with coefficients in a field is a compactly generated tensor triangulated category, that has been studied extensively in representation theory. In this paper, we provide a…

The monoids of simplicial endomorphisms, i.e. the monoids of endomorphisms in the simplicial category, are submonoids of monoids one finds in Temperley-Lieb algebras, and as the monoids of Temperley-Lieb algebras are linked to situations…

Associated to a family of $G$-$\ast$-endomorphisms on a $G$-C*-algebra $A$ satisfying certain minimality conditions, we give a $G$-C*-correspondence $\mathcal{E}$ over $A$ whose Cuntz--Pimsner algebra $\mathcal{O}_\mathcal{E}$ is simple.…

We first study commutative, pointed monoids providing basic definitions and results in a manner similar commutative ring theory. Included are results on chain conditions, primary decomposition as well as normalization for a special class of…

Skew algebroid is a natural generalization of the concept of Lie algebroid. In this paper, for a skew algebroid E, its modular class mod(E) is defined in the classical as well as in the supergeometric formulation. It is proved that there is…