arXiv math-ph/03080262003-08-22math-phhep-thmath.MPmath.QAquant-ph

Polynomial Algebras and their Applications

Bindu A. Bambah

备注：: Invited talk at "The International conference on Supersymmetric Quantum Mechanics, Valladolid Spain (July 15-20, 2003),. Work done with Dr. V. SuniKumar IOP, Bhubaneshwar and Prof. R. Jagannathan, IMSC, Chennai. 12 pages LATEX with JHEP3.cls Macro included

英文摘要：

A way to construct and classify the three dimensional polynomially deformed algebras is given and the irreducible representations is presented. for the quadratic algebras 4 different algebras are obtained and for cubic algebras 12 different classes are constructed. Applications to quantum mechanical systems including supersymmetric quantum mechanics are discussed

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Classifying finite-dimensional C-algebras by posets of their commutative C-subalgebras

We consider the functor C that to a unital C*-algebra A assigns the partial order set C(A) of its commutative C*-subalgebras ordered by inclusion. We investigate how some C*-algebraic properties translate under the action of C to order-theoretical properties. In particular, we show that A is finite dimensional if and only C(A) satisfies certain chain conditions. We eventually show that if A and B are C*-algebras such that A is finite dimensional and C(A) and C(B) are order isomorphic, then A and B must be *-isomorphic.

2016-10-06math-phmath.MPmath.OA

Superintegrability and higher order polynomial algebras I

We present a method to obtain higher order integrals and polynomial algebras for two-dimensional superintegrable systems from creation and annihilation operators. All potentials with a second and a third order integrals of motion separable in Cartesian coordinates were studied. The integrals of motion of two of them do not generate a cubic algebra. We construct for these Hamiltonians a higher order polynomial algebra from the creation and annihilation operators. We obtain quintic and seventh order polynomial algebras. We give also for polynomial algebras of order 7 realizations in terms of def…

2009-08-30hep-thmath-phmath.MP

Applications of Polynomial Algebras to Deformed Oscillator

The polynomial algebra is a deformed SU(2) algebra. Here, we use polynomial algebra as a method to solve a series of deformed oscillators. Meanwhile, we find a series of physics systems corresponding with polynomial algebra with different maximal order.

2009-10-20math-phmath.MP

Classification of Harish-Chandra modules over some Lie algebras related to the Virasoro algebra

In this paper, we provide a uniform method to thoroughly classify all Harish-Chandra modules over some Lie algebras related to the Virasoro algebras. We first classify such modules over the Lie algebra $W(\varrho)[s]$ for $s=0,\frac12$. With this result and method, we can also do such works for some Lie algebras and superconformal algebras related to the Virasoro algebra, including the several kinds of Schrödinger-Virasoro Lie algebras, which are open up to now.

2015-10-27math-phmath.MPmath.QA

On realizations of polynomial algebras with three generators via deformed oscillator algebras

We present the most general polynomial Lie algebra generated by a second order integral of motion and one of order M, construct the Casimir operator, and show how the Jacobi identity provides the existence of a realization in terms of deformed oscillator algebra. We also present the classical analog of this construction for the most general Polynomial Poisson algebra. Two specific classes of such polynomial algebras are discussed that include the symmetry algebras observed for various 2D superintegrable systems.

2014-02-14math-phmath.MP

Representations and cohomologies of relative Rota-Baxter Lie algebras and applications

In this paper, first we give the notion of a representation of a relative Rota-Baxter Lie algebra and introduce the cohomologies of a relative Rota-Baxter Lie algebra with coefficients in a representation. Then we classify abelian extensions of relative Rota-Baxter Lie algebras using the second cohomology group, and classify skeletal relative Rota-Baxter Lie 2-algebras using the third cohomology group as applications. At last, using the established general framework of representations and cohomologies of relative Rota-Baxter Lie algebras, we give the notion of representations of Rota-Baxter Li…

2021-08-16math-phmath.MPmath.RA

更多相关论文收起更多论文

The Kepler problem: polynomial algebra of non-polynomial first integrals

The sum of elliptic integrals simultaneously determines orbits in thr Kepler problem and the addition of divisors on elliptic curves. Periodic motion of a body in physical space is defined by symmetries, whereas periodic motion of divisors is defined by a fixed point on the curve. Algebra of the first integrals associated with symmetries is a well-known mathematical object, whereas algebra of the first integrals associated with coordinates of fixed points is unknown. In this paper, we discuss polynomial algebras of non-polynomial first integrals of superintegrable systems associated with ellip…

2019-03-21math-phmath.DSmath.MP