Results 41 to 50 of about 43,752 (85)

Quantum groups, Yang-Baxter maps and quasi-determinants

, 2017
For any quasi-triangular Hopf algebra, there exists the universal R-matrix, which satisfies the Yang-Baxter equation. It is known that the adjoint action of the universal R-matrix on the elements of the tensor square of the algebra constitutes a quantum ...
Tsuboi, Zengo
core   +3 more sources

Quantum algebra of multiparameter Manin matrices [PDF]

Journal of Algebra, 2023
N. Jing, Yinlong Liu, Jian Zhang
semanticscholar   +1 more source

On Hopf algebroid structure of kappa-deformed Heisenberg algebra

, 2016
The $(4+4)$-dimensional $\kappa$-deformed quantum phase space as well as its $(10+10)$-dimensional covariant extension by the Lorentz sector can be described as Heisenberg doubles: the $(10+10)$-dimensional quantum phase space is the double of $D=4 ...
Lukierski, Jerzy, Woronowicz, Mariusz, Škoda, Zoran   +2 more
core   +1 more source

Quantum Jordanian twist

, 2000
The quantum deformation of the Jordanian twist F_qJ for the standard quantum Borel algebra U_q(B) is constructed. It gives the family U_qJ(B) of quantum algebras depending on parameters x and h.
Abdesselam B, Alexander M Mirolubov, Aneva B L, Ballesteros A, Drinfeld V G, Drinfeld V G, Gerstenhaber M, Jimbo M, Jimbo M, Kac V G, Khoroshkin S M, Khoroshkin S M, Kulish P P, Kulish P P, Kulish P P, Kulish P P, Kulish P P, Kupershmidt B A, Lyakhovsky V D, Lyakhovsky V D, Lyakhovsky V D, Mariano A del Olmo, Ogievetsky O V, Ogievetsky O V, Reshetikhin N Yu, Stolin A, Vladimir D Lyakhovsky   +26 more
core   +1 more source

Topological Hopf algebras, quantum groups and deformation quantization

, 2003
After a presentation of the context and a brief reminder of deformation quantization, we indicate how the introduction of natural topological vector space topologies on Hopf algebras associated with Poisson Lie groups, Lie bialgebras and their doubles ...
Bonneau, Philippe, Sternheimer, Daniel
core   +1 more source

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Local derivations of quantum plane algebra

Communications in Algebra, 2023
– Let k be a field and q∈k* not a root of unity. We prove that on the quantum plane algebra Pq(k)=kq[x,y] any local derivation is a derivation.
A. Louly
semanticscholar   +1 more source

Quantization of the derivation Lie algebra over quantum torus

Communications in Algebra, 2023
Recently, Lie bialgebra structures of the derivation Lie algebra over quantum torus were determined. In this paper, we use the general method of quantization by a Drinfel’d twist to quantize these algebras with their Lie bialgebra structures and present ...
Shuoyang Xu, Xiaoqing Yue
semanticscholar   +1 more source

BV Structure on Hochschild Cohomology of Quantum Exterior Algebra with Two Variables

Algebra Colloquium, 2023
Let [Formula: see text] over a field [Formula: see text]. We give a clear characterization of the Batalin-Vilkovisky algebraic structure on Hochschild cohomology of [Formula: see text] for any [Formula: see text], and the Gerstenhaber algebraic structure
B. Hou, Jinzhong Wu
semanticscholar   +1 more source

Quantum Register Algebra: the mathematical language for quantum computing

Quantum Information Processing, 2022
We present Quantum Register Algebra (QRA) as an efficient tool for quantum computing. We show the direct link between QRA and Dirac formalism. We present Geometric Algebra Algorithms Optimizer (GAALOP) implementation of our approach.
J. Hrdina, D. Hildenbrand, Aleš Návrat, Christian Steinmetz, R. Alves, C. Lavor, Petr Vašík, I. Eryganov   +7 more
semanticscholar   +1 more source

Non-standard quantum algebra Uh(sl(2,R))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {U}_h (\mathfrak {sl}

Quantum Information Processing
We discuss the application of the Jordanian quantum algebra Uh(sl(2,R))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek ...
Angel Ballesteros, J. J. Relancio, Lucia Santamaría-Sanz   +2 more
semanticscholar   +1 more source