Related papers: Actions of compact quantum groups

We show that for any co-amenable compact quantum group A=C(G) there exists a unique compact Hausdorff topology on the set EA of isomorphism classes of ergodic actions of G such that the following holds: for any continuous field of ergodic…

We show that the category A(G) of actions of a locally compact group G on C*-algebras (with equivariant nondegenerate *-homomorphisms into multiplier algebras) is equivalent, via a full-crossed-product functor, to a comma category of…

Inclusions of operator algebras have long been studied. In particular, inclusions arising from actions of compact groups on factors were studied by Izumi-Longo-Popa and others. The correspondence between intermediate subfactors and…

We show that any free action of a connected Lie group of polynomial growth on a finite dimensional locally compact space has finite tube dimension. This is shown to imply that the associated crossed product C*-algebra has finite nuclear…

We classify compact, connected Hamiltonian and quasi-Hamiltonian manifolds of cohomogeneity one (which is the same as being multiplicity free of rank one). Here the group acting is a compact connected Lie group (simply connected in the…

In this article, we give a general construction of spectral triples from certain Lie group actions on unital C*-algebras. If the group G is compact and the action is ergodic, we actually obtain a real and finitely summable spectral triple…

We study the C*-algebra crossed-product of the closed unit disk by the action of one of its conformal automorphisms. After classifying the conformal automorphisms up to topological conjugacy, we investigate, for each class, the irreducible…

This paper studies nilpotent orbits in complex simple Lie algebras from the viewpoint of strongly visible actions in the sense of T. Kobayashi. We prove that the action of a maximal compact group consisting of inner automorphisms on a…

Considering the potential equivariant formality of the left action of a connected Lie group $K$ on the homogeneous space $G/K$, we arrive through a sequence of reductions at the case $G$ is compact and simply-connected and $K$ is a torus.…

For a (unital) $C^*$-algebra $\cla$, we construct a $C^*$-algebraic discrete quantum group (DQG) $\clq_{\rm aut}(\cla)$, coacting on $\cla$, which is a quantum generalization of ${\text Aut}(\cla)$ in the framework of discrete quantum…

We initiate a careful study of a generalized symmetric imprimitivity theory for commuting proper actions of locally compact groups H and K on a C*-algebra.

We study isometric Lie group actions on symmetric spaces admitting a section, i.e. a submanifold which meets all orbits orthogonally at every intersection point. We classify such actions on the compact symmetric spaces with simple isometry…

We introduce a method to study C*-algebras possessing an action of the circle group, from the point of view of its internal structure and its K-theory. Under relatively mild conditions our structure Theorem shows that any C*-algebra, where…

Given a group G, we construct, in a canonical way, an inverse semigroup S(G) associated to G. The actions of S(G) are shown to be in one-to-one correspondence with the partial actions of G, both in the case of actions on a set, and that of…

The aim of this paper is to classify cohomogeneity one isometric actions on the 4-dimensional Minkowski space $\mathbb{R}^{3,1}$, up to orbit equivalence. Representations, up to conjugacy, of the acting groups in $O(3,1)\ltimes…

Continuous actions of topological groups on compact Hausdorff spaces $X$ are investigated which induce almost periodic functions in the corresponding commutative C*-algebra. The unique invariant mean on the group resulting from averaging…

Quantum corrections of certain types and relevant in certain regimes can be summarised in terms of an effective action calculable, in principle, from the underlying theory. The demands of symmetries, local form of terms and dimensional…

In this paper, we collect some technical results about weights on C*-algebras which are useful in de theory of locally compact quantum groups in the C*-algebra framework. We discuss the extension of a lower semi-continuous weight to a…

We give a new alternative version of the reconstruction procedure for ergodic actions of compact quantum groups and we refine it to include characterizations of (braided commutative) Yetter-Drinfeld C*-algebras. We then use this to…

In this work we investigate the notion of action or coaction of a finite quantum groupoid in von Neumann algebras context. In particular we prove a double crossed product theorem and prove the existence of an universal von Neumann algebra…