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Related papers: Quommutator deformations of spl(N,1)

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In this paper fundamental Wigner coefficients are determined algebraically by considering the eigenvalues of certain generalized Casimir invariants. Here this method is applied in the context of both type 1 and type 2 unitary…

Mathematical Physics · Physics 2017-09-13 Jason L. Werry , Phillip S. Isaac , Mark D. Gould

In this work, we recall that every filiform Lie superalgebra is a deformation of the superalgebra $L_{n,m}$. We study the even cocycles which give this nilpotent deformations. A family of independent bilinear maps will help us to describe…

Rings and Algebras · Mathematics 2007-05-23 M. Gilg

Let (\Gamma,d) be the 3D-calculus or the 4D_{\pm}-calculus on the quantum group SU_q(2). We describe all pairs (\pi, F) of a *-representation \pi of O(SU_q(2)) and of a symmetric operator F on the representation space satisfying a technical…

Quantum Algebra · Mathematics 2009-10-31 Konrad Schmuedgen

This paper deals with quon algebras or deformed oscillator algebras, for which the deformation parameter is a root of unity. We show the interest of such algebras for fractional supersymmetric quantum mechanics, angular momentum theory and…

Quantum Physics · Physics 2008-04-25 Maurice R. Kibler

We construct quantum deformation of Poincar\'e group using as a starting point $SU(2,2)$ conformal group and twistor-like definition of the Minkowski space. We obtain quantum deformation of $SU(2,2)$ as a real form of multiparametric…

High Energy Physics - Theory · Physics 2007-05-23 M. Chaichian , A. P. Demichev

In this paper Witten type deformation of osp(1/2) algbera is introduced and its realization and matrix representation are obtained. The matrix representation is shown to be possible only when the dimension is odd.

q-alg · Mathematics 2008-02-03 W-S. Chung

We compute arithmetic support of the formal deformations $D=P+tQ_1+t^2Q_2+...$ of the differential operator $P=(x\partial_x-r_1)...(x\partial_x-r_k)$, where $r_1,...,r_k\in\mathbb{Q}$ for sufficiently large primes $p$ in terms of the…

Algebraic Geometry · Mathematics 2025-05-20 Maxim Kontsevich , Alexander Odesskii

We present three groups of examples of Wigner Quantum Systems related to the Lie superalgebras $osp(1/6n)$, $sl(1/3n)$ and $sl(n/3)$ and discuss shortly their physical features. In the case of $sl(1/3n)$ we indicate that the underlying…

High Energy Physics - Theory · Physics 2009-11-07 T. D. Palev , N. I. Stoilova

A class of second order difference (discrete) operators with a partial algebraization of the spectrum is introduced. The eigenfuncions of the algebraized part of the spectrum are polinomials (discrete polinomials). Such difference operators…

Condensed Matter · Physics 2009-10-28 P. B. Wiegmann , A. V. Zabrodin

We compute the infinitesimal deformations of two families of restricted simple modular Lie algebras of Cartan type: the Witt-Jacobson and the Special Lie algebras.

Rings and Algebras · Mathematics 2009-02-07 Filippo Viviani

We study the algebra of difference operators that commute with the two-body Ruijsenaars operator, a $q$-deformation of the Lam\'e differential operator, for generic values of the deformation parameter. The algebra is commutative. It is the…

q-alg · Mathematics 2008-02-03 Giovanni Felder , Alexander Varchenko

We define the notion of a Lie superalgebra over a field $k$ of characteristic $2$ which unifies the two pre-existing ones - $\mathbb{Z}/2$-graded Lie algebras with a squaring map and Lie algebras in the Verlinde category ${\rm Ver}_4^+(k)$,…

Representation Theory · Mathematics 2025-07-24 Pavel Etingof , Serina Hu

We present a twisted commutator deformation for $N=1,2$ super Virasoro algebras based on $GL_q(1,1)$ covariant noncommutative superspace.

High Energy Physics - Theory · Physics 2009-10-30 Haru-Tada Sato

A two-parameter deformed superoscillator system with SUq1/q2(n|m)-covariance is presented and used to construct a two-parameter deformed N=2 SUSY algebra. The Fock space representation of the algebra is discussed and the deformed…

High Energy Physics - Theory · Physics 2011-07-28 Abdullah Algin , Metin Arik , Ali Serdar Arikan

In the present paper we review our project of systematic construction of invariant differential operators on the example of the non-compact algebras su(n,n) for n=2,3,4. We give explicitly the main multiplets of indecomposable elementary…

Representation Theory · Mathematics 2015-06-23 V. K. Dobrev

We study the relations between $q$-deformations and $q$-coherent states of the single oscillator representations for $su_q(1,1)$ and $su_q(2)$ algebras; Dyson and Holstein-Primakoff type in terms of Biedenharn, Macfarlane and anyonic…

q-alg · Mathematics 2008-11-26 Phillial Oh , Chaiho Rim

We consider Poisson superalgebras with constant nondegenerate bracket realized on the smooth Grassmann-valued functions with compact supports in R^{2n}. The deformations with even and odd deformation parameters of these superalgebras are…

Quantum Algebra · Mathematics 2010-01-13 S. E. Konstein , I. V. Tyutin

We overview classifications of simple infinite-dimensional complex $\mathbb{Z}$-graded Lie (super)algebras of polynomial growth, and their deformations. A subset of such Lie (super)algebras consist of vectorial Lie (super)algebras whose…

Representation Theory · Mathematics 2024-06-25 Dimitry Leites , Irina Shchepochkina

n-ary algebras have played important roles in mathematics and mathematical physics. The purpose of this paper is to construct a deformation of Virasoro-Witt n-algebra based on an oscillator realization with two independent parameters (p, q)…

Mathematical Physics · Physics 2016-02-26 Xiao-Yu Jia , Lu Ding , Zhao-Wen Yan , Shi-Kun Wang

The $q$-deformation of the infinite-dimensional $n$-algebra is investigated. Based on the structure of the $q$-deformed Virasoro-Witt algebra, we derive a nontrivial $q$-deformed Virasoro-Witt $n$-algebra which is nothing but a sh-$n$-Lie…

High Energy Physics - Theory · Physics 2015-06-30 Lu Ding , Xiao-Yu Jia , Ke Wu , Zhao-Wen Yan , Wei-Zhong Zhao