5 citations · 11 across the 10 of their papers we have counts for
11 papers
Geometric construction of superintegrable Poisson projection chains via Poisson centralizers
Kai Jiang, Guorui Ma, Ian Marquette +2
We introduce a geometric framework for constructing superintegrable systems from Poisson centralizers (commutants) in the Lie-Poisson algebra of a complex semisim…
Poisson Centralisers and Polynomial Superintegrability for Magnetic Geodesic Flows on Reductive Homogeneous Spaces
Kai Jiang, Guorui Ma, Ian Marquette +2
We provide a method for formulating superintegrable magnetic geodesic flows on reductive homogeneous spaces , with a compact semisimple Lie group and a closed subgro…
Subalgebra chains and nuclear physics: Commutant approach and construction of polynomial algebras
Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette +2
In this paper, we review a new approach to study subalgebra chains in the context of nuclear physics. This approach does not rely on explicit r…
Polynomial algebra from the Lie algebra reduction chain : The supermultiplet model
Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette +2
The supermultiplet model, based on the reduction chain , is revisited through the lens of commutants within unive…
On the construction of polynomial Poisson algebras: a novel grading approach
Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette +2
In this work, we refine recent results on the explicit construction of polynomial algebras associated with commutants of subalgebras in enveloping algebras of Lie algebras by consi…
Polynomial Poisson Algebras and Superintegrable Systems from Cartan centralisers of Types , and
Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette +2
In this work, we construct explicit formulas for the generators of the Cartan centralisers of complex semisimple Lie algebras and , the case being already know…
On polynomial symmetry algebras underlying superintegrable systems in Darboux spaces
Ian Marquette, Junze Zhang, Yao-Zhong Zhang
We review three different approaches to polynomial symmetry algebras underlying superintegrable systems in Darboux spaces. The first method consists of using deformed oscillator al…
Algebraic structures and Hamiltonians from the equivalence classes of 2D conformal algebras
Ian Marquette, Junze Zhang, Yao-Zhong Zhang
The construction of superintegrable systems based on Lie algebras and their universal enveloping algebras has been widely studied over the past decades. However, most constructions…
Infinite dimensional representations of cubic and quintic algebras and special functions
Ian Marquette, Junze Zhang, Yao-Zhong Zhang
Finite and Infinite-dimensional representations of symmetry algebras play a significant role in determining the spectral properties of physical Hamiltonians. In this paper, we intr…
Algebraic approach and exact solutions of superintegrable systems in 2D Darboux spaces
Ian Marquette, Junze Zhang, Yao-Zhong Zhang
Superintegrable systems in 2D Darboux spaces were classified and it was found that there exist 12 distinct classes of superintegrable systems with quadratic integrals of motion (an…
Complex structures on stratified Lie algebras
Junze Zhang
This paper investigates some properties of complex structures on Lie algebras. In particular, we focus on that are characterized…