Related papers: On the conjugation action for quantum general line…
We establish a quantum Galois correspondence for compact Lie groups of automorphisms acting on a simple vertex operator algebra.
In 1999, Brylinski and Zhang computed the complex equivariant K-theory of the conjugation self-action of a compact, connected Lie group with torsion-free fundamental group. In this note we show it is possible to do so in under a page.
We analyze the problem of general covariance for quantum gravity theories in the background field formalism with respect to gauge fixing procedure. We prove that the background effective action is not invariant under general coordinate…
The groupoid approach to noncommutative unification of general relativity with quantum mechanics is compared with the canonical gravity quantization. It is shown that by restricting the corresponding noncommutative algebra to its…
We address the joint estimation of changes in the position and linear momentum of a quantum particle or, equivalently, changes in the complex field of a bosonic mode. Although these changes are generated by non-commuting operators, we show…
In this paper we will find a matrix realizations of the quantum group g_{p, q}. For this purpose, we construct all primitive idempotents and a basis of g_{p, q}. We determine the action of elements of the basis on the indecomposable…
Let $\mathcal{G}$ be an algebraic quantum group. We introduce an equivariant algebraic $kk$-theory for $\mathcal{G}$-module algebras. We study an adjointness theorem related with smash product and trivial action. We also discuss a duality…
Given an action of a Compact Quantum Group (CQG) on a finite dimensional Hilbert space, we can construct an action on the associated Cuntz algebra. We study the fixed point algebra of this action, using Kirchberg classification results.…
The gauge gravity action for general relativity in any dimension using a connection for the Euclidean or Poincar\'e group and a symmetry-breaking scalar field is written using a particularly simple matrix technique. A discrete version of…
We study linear actions of finite groups in small dimensions, up to equivariant birationality.
We provide a unified framework for nonsignalling quantum and classical multipartite correlations, allowing all to be written as the trace of some local (quantum) measurements multiplied by an operator. The properties of this operator define…
In this article, we introduce the concept of partial actions of a group $G$ on quivers and demonstrate that for any given partial action of G on a quiver $\Gamma$, there exists another quiver, $\Gamma'$ with a full $G$-action. This is an…
The notion of an action of a locally compact quantum group on a von Neumann algebra is studied from the amenability point of view. Various Reiter's conditions for such an action are discussed. Several applications to some specific actions…
Global internal symmetries act unitarily on local observables or states of a quantum system. In this note, we aim to generalise this statement to extended observables by considering unitary actions of finite global 2-group symmetries…
We introduce an algorithm for designing Neural Group Actions, collections of deep neural network architectures which model symmetric transformations satisfying the laws of a given finite group. This generalizes involutive neural networks…
Generalized quantum cluster algebras introduced in [1] are quantum deformation of generalized cluster algebras of geometric types. In this paper, we prove that the Laurent phenomenon holds in these generalized quantum cluster algebras. We…
Starting from a local quantum field theory with an unbroken compact symmetry group $G$ in 1+1-dimensional spacetime we construct disorder fields implementing gauge transformations on the fields (order variables) localized in a wedge region.…
Working towards an algebra for operators of strongly interacting quantum fields, a nonassociative decomposition of field operators is proposed. In the demonstrated case, quantum corrections appear from the possible bracket permutations. A…
We outline in detail the general caloron correspondence for the group of automorphisms of an arbitrary principal $G$-bundle $Q$ over a manifold $X$, including the case of the gauge group of $Q$. These results are used to define…
We give a brief overview of the properties of a higher dimensional generalization of matrix model which arises naturally in the context of a background independent approach to quantum gravity, the so called group field theory. We show that…