Related papers: Twisted Crossed Products and Magnetic Pseudodiffer…
For a twisted partial action \Theta of a group G on an (associative non-necessarily unital) algebra A over a commutative unital ring k, the crossed product A X_\Theta G is proved to be associative. Given a G-graded k-algebra B =…
We aim at constructing an analog of the Weyl calculus in an infinite dimensional setting, in which the usual configuration and phase spaces are ultimately replaced by infinite dimensional measure spaces, the so-called abstract Wiener…
We consider group actions of topological groups on C*-algebras of the types which occur in many physics models. These are singular actions in the sense that they need not be strongly continuous, or the group need not be locally compact. We…
We decompose the crossed product functor for actions of crossed modules of locally compact groups on C*-algebras into more elementary constructions: taking crossed products by group actions and fibres in C*-algebras over topological spaces.…
We present a comparison of the noncommutative field theories built using two different star products: Moyal and Wick-Voros (or normally ordered). For the latter we discuss both the classical and the quantum field theory in the quartic…
Partial dynamical systems (X,alpha) arise naturally when dealing with commutative C*-dynamical system (A,delta). We associate with every pair (X,alpha), or (A,delta), a covariance C*-algebra C*(X,alpha)=C*(A,delta) which agrees with a…
The notions of Busby-Smith and Green type twisted actions are extended to discrete unital inverse semigroups. The connection between the two types, and the connection with twisted partial actions, are investigated. Decomposition theorems…
Deformation theory refers to an apparatus in many parts of math and physics for going from an infinitesimal (= first order) deformation to a full deformation, either formal or convergent appropriately. If the algebra being deformed is that…
In this paper, we give some properties of the fixed point algebra and the crossed product of a unital separable simple infinite dimensional C*-algebra by an action of a second-countable compact group with the tracial Rokhlin property with…
In this article a new formulation of the Weyl C*-algebra, which has been invented by Fleischhack, in terms of C*-dynamical systems is presented. The quantum configuration variables are given by the holonomies along paths in a graph.…
Let P be a left LCM semigroup, and $\alpha$ an action of $P$ by endomorphisms of a $C^{*}$-algebra $A$. We study a semigroup crossed product $C^{*}$-algebra in which the action $\alpha$ is implemented by partial isometries. This crossed…
We take a new look at dilation theory for nonself-adjoint operator algebras. Among the extremal (co)extensions of a representation, there is a special property of being fully extremal. This allows a refinement of some of the classical…
I combine recent results in the structure theory of nuclear C*-algebras and in topological dynamics to classify certain types of crossed products in terms of their Elliott invariants. In particular, transformation group C*-algebras…
We study the interplay of interactions and topology in a pseudo-spin Weyl system, obtained from a minimally modified Hubbard model, using the numerically exact auxiliary-field quantum Monte Carlo method complemented by mean-field theory. We…
We formulate a Mayer--Vietoris/\v{C}ech viewpoint on $K$-theory for crossed products by discrete quantum groups, emphasizing how local-to-global gluing data interacts with quantum-group coefficients. Starting from a $G$-equivariant ideal…
This article presents a survey of recent developments on pseudodifferential operators on noncommutative tori. We describe currently available constructions of those operators: by means of a $C^*$--dynamical system, by using an analogue of…
Using general principles of the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an…
This article is concerned with crossed products and their applications to random operators. We study the von Neumann algebra of a dynamical system using the underlying Hilbert algebra structure. This gives a particularly easy way to…
We study the asymptotic behavior of the counting function of tensor products of operators, in the cases where the factors are either pseudodifferential operators on closed manifolds, or pseudodifferential operators of Shubin type on…
Let a discrete group $G$ act on a unital simple C$^*$-algebra $A$ by outer automorphisms. We establish a Galois correspondence $H\mapsto A\rtimes_{\alpha,r}H$ between subgroups of $G$ and C$^*$-algebras $B$ satisfying $A\subseteq B…