Results 31 to 40 of about 68,205 (182)

Lie polynomials in q-deformed Heisenberg algebras [PDF]

Journal of Algebra, 2019
Let $\mathbb{F}$ be a field, and let $q\in\mathbb{F}$. The $q$-deformed Heisenberg algebra is the unital associative $\mathbb{F}$-algebra $\mathcal{H}(q)$ with generators $A,B$ and relation $AB-qBA=I$, where $I$ is the multiplicative identity in $\mathcal{H}(q)$.
openaire   +2 more sources

Noncomplete affine structures on Lie algebras of maximal class

International Journal of Mathematics and Mathematical Sciences, 2002
Every affine structure on Lie algebra 𝔤 defines a representation of 𝔤 in aff(ℝn). If 𝔤 is a nilpotent Lie algebra provided with a complete affine structure then the corresponding representation is nilpotent.
E. Remm, Michel Goze
doaj   +1 more source

The Harmonic Oscillator on the Heisenberg Group

Comptes Rendus. Mathématique, 2020
In this note we present a notion of harmonic oscillator on the Heisenberg group $\mathbf{H}_n$ which forms the natural analogue of the harmonic oscillator on $\mathbb{R}^n$ under a few reasonable assumptions: the harmonic oscillator on $\mathbf{H}_n ...
Rottensteiner, David, Ruzhansky, Michael
doaj   +1 more source

The structure, capability and the Schur multiplier of generalized Heisenberg Lie algebras [PDF]

Journal of Algebra, 2017
From [Problem 1729, Groups of prime power order, Vol. 3], Berkovich et al. asked to obtain the Schur multiplier and the representation of a group $G$, when $G$ is a special $p$-group minimally generated by $d$ elements and $|G'|=p^{\frac{1}{2}d(d-1 ...
P. Niroomand, F. Johari
semanticscholar   +1 more source

Cohomology of Heisenberg Lie algebras [PDF]

Proceedings of the American Mathematical Society, 1983
The cohomology of Heisenberg Lie algebras is studied and we obtain the description of cocycles, coboundaries and cohomological spaces.
openaire   +1 more source

Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach

Physics Letters B, 2018
We consider new Abelian twists of Poincare algebra describing nonsymmetric generalization of the ones given in [1], which lead to the class of Lie-deformed quantum Minkowski spaces.
Jerzy Lukierski, Daniel Meljanac, Stjepan Meljanac, Danijel Pikutić, Mariusz Woronowicz   +4 more
doaj   +1 more source

Deformation of the Heisenberg–Weyl algebra and the Lie superalgebra osp1|2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{documen [PDF]

The European Physical Journal Plus
We propose a new deformation of the quantum harmonic oscillator Heisenberg–Weyl algebra with a parameter a>-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy ...
E. Jafarov, S. Nagiyev, J. Van der Jeugt
semanticscholar   +1 more source

Torsion-Type q-Deformed Heisenberg Algebra and Its Lie Polynomials [PDF]

Springer Proceedings in Mathematics & statistics, 2017
Given a scalar parameter q, the q-deformed Heisenberg algebra \(\mathcal {H}(q)\) is the unital associative algebra with two generators A, B that satisfy the q-deformed commutation relation \(AB-qBA=I\), where \(I\) is the multiplicative identity. For \(\
R. Cantuba, S. Silvestrov
semanticscholar   +1 more source

The Invariant Two-Parameter Function of Algebras ψ

Mathematical and Computational Applications, 2019
At present, the research on invariant functions for algebras is very extended since Hrivnák and Novotný defined in 2007 the invariant functions ψ and φ as a tool to study the Inönü−Wigner contractions (IW ...
José María Escobar, Juan Núñez-Valdés, Pedro Pérez-Fernández   +2 more
doaj   +1 more source

Compact Manifolds With Unbounded Nilpotent Fundamental Groups and Positive Ricci Curvature

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT It follows from the work of Kapovitch and Wilking that a closed manifold with nonnegative Ricci curvature has a uniformly almost nilpotent fundamental group. Leftover questions and conjectures, have asked if in this context the fundamental group is actually uniformly almost abelian. The main goal of this work is to construct examples (Mk9,gk)$(
Elia Bruè, Aaron Naber, Daniele Semola
wiley   +1 more source