Related papers: AQV IV. A new formulation of the holonomy-flux *-a…
There are theories of coverings of $C^*$-algebras which can be included into a following list: coverings of commutative $C^*$-algebras, coverings of $C^*$-algebras of groupoids and foliations, coverings of noncommutative tori, the double…
Much of the work in loop quantum gravity and quantum geometry rests on a mathematically rigorous integration theory on spaces of distributional connections. Most notably, a diffeomorphism invariant representation of the algebra of basic…
We study connections among polynomials, differential equations and streams over a field K, in terms of algebra and coalgebra. We first introduce the class of (F,G)-products on streams, those where the stream derivative of a product can be…
We develop an algebraic and operational framework for quantum isomorphisms of hypergraphs, using tools from compact quantum group theory. We introduce a new synchronous version of the hypergraph isomorphism game whose game algebra uniformly…
We construct in this article a new realization of quantum geometry, which is obtained by quantizing the recently-introduced flux formulation of loop quantum gravity. In this framework, the vacuum is peaked on flat connections, and states…
We introduce a notion of Rokhlin dimension for one parameter automorphism groups of C*-algebras. This generalizes Kishimoto's Rokhlin property for flows, and is analogous to the notion of Rokhlin dimension for actions of the integers and…
We study formal deformations of a crossed product $S(V)#_f G$, of a polynomial algebra with a group, induced from a universal deformation formula introduced by Witherspoon. These deformations arise from braided actions of Hopf algebras…
Given a closed ideal I in a C*-algebra A, an ideal J (not necessarily closed) in I, a *-homomorphism \al:A --> M(I) and a map L:J --> A with some properties, based on [3] and [9] we define a C*-algebra O(A,\al,L) which we call the "Crossed…
In this paper, we study and classify Hilbert space representations of cross product *-algebras of the quantized enveloping algebra $U_q(e_2)$ with the coordinate algebras $O(E_q(2))$ of the quantum motion group and $O(\C_q)$ of the complex…
A cosystem consists of a possibly nonselfadoint operator algebra equipped with a coaction by a discrete group. We introduce the concept of C*-envelope for a cosystem; roughly speaking, this is the smallest C*-algebraic cosystem that…
For q generic or a primitive l-th root of unity, q-Witt algebras are described by means of q-divided power algebras. The structure of the universal q-central extension of the q-Witt algebra, the q-Virasoro algebra, is also determined. q-Lie…
Different graphical calculi have been proposed to represent quantum computation. First the ZX- calculus [4], followed by the ZW-calculus [12] and then the ZH-calculus [1]. We can wonder if new Z*-calculi will continue to be proposed…
Confluence in abstract parallel category systems is established for net class-rewriting in iterative closed multilevel quotient graph structures with uncountable node arities by multi-dimensional transducer operations in topological metrics…
In this paper we introduce a new algebraic device, which enables us to treat the quaternions as though they were a commutative field. This is of interest both for its own sake, and because it can be applied to develop an "algebraic…
The completion $\overline{A}[\tau]$ of a locally convex *-algebra $A [ \tau ]$ with not jointly continuous multiplication is a *-vector space with partial multiplication $xy$ defined only for $x$ or $y \in A_{0}$, and it is called a…
It is known that the involution corresponding to the compact form is incompatible with comultiplication for quantum groups at $|q|=1$. In this paper we consider the quantum algebra of functions on the deformed space $T^{*}G_{q}$ which…
We give a new definition of the semigroup C*-algebra of a left cancellative semigroup, which resolves problems of the construction by X. Li. Namely, the new construction is functorial, and the independence of ideals in the semigroup does…
We consider an action of the circle group, T on a von Neumann algebra, M. Similarly to the case when the algebra of essentially bounded functions on T is acted upon by translations, we define the generalized Hardy subspace of H,where H is…
We propose an abstract framework of a kind of representation theory for $C^*$-flows, i.e., $C^*$-algebras equipped with one-parameter automorphism groups, as a proper generalization of Olshanski's formalism of unitary representation theory…
It is easy to see that every character (i.e. unital *-homomorphism to the complex numbers) of a commutative unital associative *-algebra is a pure state (i.e. extreme point in the convex set of all normalized positive linear functionals).…