Related papers: The generalized Racah algebra as a commutant
Let R be an associative ring.In the paper we study n-generalized commutators of rings and prove that if R is a noncommutative prime ring and n > 2, then every nonzero n-generalized Lie ideal of R contains a nonzero ideal. Therefore, if R is…
This note being devoted to some aspects of the inverse problem of representation theory explicates the links between researches on the Sklyanin algebras and the author's (based on the noncommutative geometry) approach to the setting free of…
We consider the polynomial representation of Double Affine Hecke Algebras (DAHAs) and construct its submodules as ideals of functions vanishing on the special collections of affine planes. This generalizes certain results of Kasatani in…
An abstract Newton-like equation on a general Lie algebra is introduced such that orbits of the Lie-group action are attracting set. This equation generates the nonlinear dynamical system satisfied by the group parameters having an…
Let $R=\oplus_{\Gamma\in\Gamma}R_{\gamma}$ be a $\Gamma$-graded $K$-algebra over a field $K$, where $\Gamma$ is a totally ordered semigroup, and let $I$ be an ideal of $R$. Considering the $\Gamma$-grading filtration $FR$ of $R$ and the…
Given a finite-index and finite-depth subfactor, we define the notion of \textit{quantum double inclusion} - a certain unital inclusion of von Neumann algebras constructed from the given subfactor - which is closely related to that of…
Every real simple non-compact Lie algebra not isomorphic to $\mathfrak{so}(1,n)$ contains a unique standard parabolic subalgebra whose nilradical is a generalized Heisenberg algebra. Here we discuss the associated parabolic geometries and…
In this paper, we give the definition of the generalized Ramond N=2 superconformal algebras and discuss the derivation algebra and the automorphism group
We describe basic concepts of noncommutative geometry and a general construction extending the familiar duality between ordinary spaces and commutative algebras to a duality between Quotient spaces and Noncommutative algebras. Basic tools…
This paper deals with bases in a finite-dimensional Hilbert space. Such a space can be realized as a subspace of the representation space of SU(2) corresponding to an irreducible representation of SU(2). The representation theory of SU(2)…
For associative commutative algebras $A$ with Rota-Baxter operator $R$ identities of the algebra $AR=(A,\circ)$, where $a\circ b= aR(b),$ are found.
For the semisimple Lie algebra $ \frak{sl}_n$, the basic representation $L_{\widehat{\frak{sl}_{n}}}(1,0)$ of the affine Lie algebra $\widehat{\frak{sl}_{n}}$ is a lattice vertex operator algebra. The first main result of the paper is to…
It has been known since 2007 that the Wilson and Racah polynomials can be characterized as basis functions for irreducible representations of the quadratic symmetry algebra of the quantum superintegrable system on the 2-sphere,…
The representation theory of the generalized deformed oscillator algebras (GDOA's) is developed. GDOA's are generated by the four operators ${1,a,a^{\dag},N}$. Their commutators and Hermiticity properties are those of the boson oscillator…
We study some q-analogues of the Racah polynomials and some of their applications in the theory of representation of quantum algebras.
We perform an Hamiltonian reduction on a classical \cw(\cg, \ch) algebra, and prove that we get another \cw(\cg, \ch$'$) algebra, with $\ch\subset\ch'$. In the case $\cg=S\ell(n)$, the existence of a suitable gauge, called Generalized…
We give a presentation of Schur algebras (over the rational number field) by generators and relations, in fact a presentation which is compatible with Serre's presentation of the universal enveloping algebra of a simple Lie algebra. In the…
We construct explicitly a Kac-Moody algebra associated to SL$(2, \mathbb R)$ in two different but equivalent ways: either by identifying a Hilbert basis of $L^2($SL$(2, \mathbb R))$ or by the Plancherel Theorem. Central extensions and…
In the previous works \cite{N46,N47} authors have defined the oscillator-like system that associated with the two variable Chebyshev-Koornwinder polynomials. We call this system the generalized Chebyshev - Koornwinder oscillator. In this…
A 2-Hilbert space is a category with structures and properties analogous to those of a Hilbert space. More precisely, we define a 2-Hilbert space to be an abelian category enriched over Hilb with a *-structure, conjugate-linear on the…