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Introduction to the Yang-Baxter Equation with Open Problems

Axioms, 2012
The Yang-Baxter equation first appeared in theoretical physics, in a paper by the Nobel laureate C. N. Yang, and in statistical mechanics, in R. J. Baxter’s work.
Florin Nichita
doaj   +1 more source

Covariantization of quantized calculi over quantum groups [PDF]

Mathematica Bohemica, 2020
We introduce a method for construction of a covariant differential calculus over a Hopf algebra $A$ from a quantized calculus $da=[D,a]$, $a\in A$, where $D$ is a candidate for a Dirac operator for $A$.
Seyed Ebrahim Akrami, Shervin Farzi
doaj   +1 more source

Photon-Added Deformed Peremolov Coherent States and Quantum Entanglement

Axioms
In the present article, we build the excitedcoherent states associated with deformed su(1,1) algebra (DSUA), called photon-added deformed Perelomov coherent states (PA-DPCSs).
Kamal Berrada
doaj   +1 more source

Quantum exponentials for the modular double and applications in gravity models

Journal of High Energy Physics, 2023
In this note, we propose a decomposition of the quantum matrix group SL q + $$ {\textrm{SL}}_q^{+} $$ (2, ℝ) as (deformed) exponentiation of the quantum algebra generators of Faddeev’s modular double of U q ( sl $$ \mathfrak{sl} $$ (2, ℝ)).
Thomas G. Mertens
doaj   +1 more source

Braided C*-quantum groups

, 2019
We propose a general theory of braided quantum groups in the C*-algebraic framework using the language of multiplicative unitaries. More precisely, we construct C*-quantum groups in the monoidal category of Yetter-Drinfeld C*-algebras over regular C ...
Roy, Sutanu
core   +1 more source

Eisenstein series and quantum groups [PDF]

, 2016
We sketch a proof of a conjecture of [FFKM] that relates the geometric Eisenstein series sheaf with semi-infinite cohomology of the small quantum group with coefficients in the tilting module for the big quantum ...
Gaitsgory, Dennis
core   +3 more sources

Affine Quantum Groups

, 2006
Contribution to the Encyclopedia of Mathematical ...
Delius, G. W., MacKay, N. J.
openaire   +2 more sources

L\'evy Processes on Quantum Permutation Groups

, 2016
We describe basic motivations behind quantum or noncommutative probability, introduce quantum L\'evy processes on compact quantum groups, and discuss several aspects of the study of the latter in the example of quantum permutation groups.
Franz, Uwe, Kula, Anna, Skalski, Adam
core   +1 more source

The intertwiner spaces of non-easy group-theoretical quantum groups

, 2020
In 2015, Raum and Weber gave a definition of group-theoretical quantum groups, a class of compact matrix quantum groups with a certain presentation as semi-direct product quantum groups, and studied the case of easy quantum groups.
Maassen, Laura
core   +1 more source

ALGEBRAIC QUANTUM PERMUTATION GROUPS [PDF]

Asian-European Journal of Mathematics, 2008
We discuss some algebraic aspects of quantum permutation groups, working over arbitrary fields. If 𝕂 is any characteristic zero field, we show that there exists a universal cosemisimple Hopf algebra coacting on the diagonal algebra 𝕂n: this is a refinement of Wang's universality theorem for the (compact) quantum permutation group.
openaire   +4 more sources