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Related papers: A twisted spectral triple for quantum SU(2)

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Non-commutative Quantum Mechanics in 3D is investigated in the framework of the abelian Drinfeld twist which deforms a given Hopf algebra while preserving its Hopf algebra structure. Composite operators (of coordinates and momenta) entering…

High Energy Physics - Theory · Physics 2011-05-05 B. Chakraborty , Z. Kuznetsova , F. Toppan

Given a group $G$ and a partial factor set $\sigma $ of $G,$ we introduce the twisted partial group algebra $\kappa_{par}^{\sigma}G,$ which governs the partial projective $\sigma$-representations of $G$ into algebras over a filed $\kappa.$…

Rings and Algebras · Mathematics 2023-11-29 Mikhailo Dokuchaev , Emmanuel Jerez

We show that the structure of an almost-commutative spectral triple emerges in a semi-classical limit from a geometric construction on a configuration space of gauge connections. The geometric construction resembles that of a spectral…

High Energy Physics - Theory · Physics 2025-04-07 Johannes Aastrup , Jesper M. Grimstrup

The machinery of noncommutative geometry is applied to a space of connections. A noncommutative function algebra of loops closely related to holonomy loops is investigated. The space of connections is identified as a projective limit of…

High Energy Physics - Theory · Physics 2009-11-11 Johannes Aastrup , Jesper M. Grimstrup

In this paper we consider the problem of deformation quantization of the algebra of polynomial functions on coadjoint orbits of semisimple lie groups. The deformation of an orbit is realized by taking the quotient of the universal…

Quantum Algebra · Mathematics 2007-05-23 R. Fioresi , M. A. Lledo

We show that some factors of the universal R-matrix generate a family of twistings for the standard Hopf structure of any quantized contragredient Lie (super)algebra of finite growth. As an application we prove that any two isomorphic…

High Energy Physics - Theory · Physics 2008-02-03 Sergei Khoroshkin , Valeriy N. Tolstoy

A quantum sl(2,R) coalgebra is shown to underly the construction of a large class of superintegrable potentials on 3D curved spaces, that include the non-constant curvature analogues of the spherical, hyperbolic and (anti-)de Sitter spaces.…

Mathematical Physics · Physics 2014-11-18 Angel Ballesteros , Alberto Enciso , Francisco J. Herranz , Orlando Ragnisco

We investigate quantum deformation of conformal algebras by constructing the quantum space for $sl_q(4,C)$. The differential calculus on the quantum space and the action of the quantum generators are studied. We derive deformed $su(4)$ and…

High Energy Physics - Theory · Physics 2009-10-22 Tatsuo Kobayashi , Tsuneo Uematsu

This paper deals with several technical issues of non-perturbative four-dimensional Lorentzian canonical quantum gravity in the continuum that arose in connection with the recently constructed Wheeler-DeWitt quantum constraint operator. 1)…

General Relativity and Quantum Cosmology · Physics 2009-10-30 Thomas Thiemann

Noncommutative geometry provides both a unified description of the Standard Model of particle physics together with Einstein-Hilbert action (in euclidean signature) and some tools to go beyond the Standard Model. In this paper, we extend to…

Mathematical Physics · Physics 2021-07-21 Manuele Filaci , Pierre Martinetti , Simone Pesco

In [CPR2], we presented a K-theoretic approach to finding invariants of algebras with no non-trivial traces. This paper presents a new example that is more typical of the generic situation. This is the case of an algebra that admits only…

Operator Algebras · Mathematics 2015-05-13 A. L. Carey , A. Rennie , K. Tong

We introduce twisted Steinberg algebras over a commutative unital ring $R$. These generalise Steinberg algebras and are a purely algebraic analogue of Renault's twisted groupoid C*-algebras. In particular, for each ample Hausdorff groupoid…

Rings and Algebras · Mathematics 2022-06-06 Becky Armstrong , Lisa Orloff Clark , Kristin Courtney , Ying-Fen Lin , Kathryn McCormick , Jacqui Ramagge

This paper is to study what we call twisted regular representations for vertex operator algebras. Let $V$ be a vertex operator algebra, let $\sigma_1,\sigma_2$ be commuting finite-order automorphisms of $V$ and let…

Quantum Algebra · Mathematics 2022-06-08 Haisheng Li , Jiancai Sun

We define homology of ternary algebras satisfying axioms derived from particle scattering or, equivalently, from the third Reidemeister move. We show that ternary quasigroups satisfying these axioms appear naturally in invariants of…

Geometric Topology · Mathematics 2020-11-11 Maciej Niebrzydowski

The pseudospectra (or spectral instability) of non-selfadjoint operators is a topic of current interest in applied mathematics. In fact, for non-selfadjoint operators the resolvent could be very large outside the spectrum, making the…

Analysis of PDEs · Mathematics 2010-03-05 Nils Dencker

We study the symmetries of the soliton spectrum of a pair of T-dual integrable models, invariant under global $SL(2)_q\otimes U(1)$ transformations. They represent an integrable perturbation of the reduced Gepner parafermions, based on…

High Energy Physics - Theory · Physics 2009-11-10 J. F. Gomes , G. M. Sotkov , A. H. Zimerman

The deformed $\mathcal W$ algebras of type $\textsf{A}$ have a uniform description in terms of the quantum toroidal $\mathfrak{gl}_1$ algebra $\mathcal E$. We introduce a comodule algebra $\mathcal K$ over $\mathcal E$ which gives a uniform…

Quantum Algebra · Mathematics 2021-06-23 B. Feigin , M. Jimbo , E. Mukhin , I. Vilkoviskiy

The homotopy groups of a commutative algebra in spectra form a commutative algebra in the symmetric monoidal category of graded abelian groups. The grading and the Koszul sign rule are remnants of the structure encoded by anima as opposed…

Number Theory · Mathematics 2023-04-27 Lars Hesselholt , Piotr Pstragowski

Twisted spectral triples are a twisting of the notion of spectral triple aiming at dealing with some type III geometric situations. In the first part of the paper, we give a geometric construction of the index map of a twisted spectral…

Operator Algebras · Mathematics 2016-06-08 Raphael Ponge , Hang Wang

We construct a family of self-adjoint operators D_N which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space CP_q(l), for any l>1 and 0<q<1. They provide 0^+ dimensional equivariant…

Quantum Algebra · Mathematics 2010-06-01 Francesco D'Andrea , Ludwik Dabrowski