Polynomial algebras from Lie algebra reduction chains <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si315.svg" display="inline" id="d1e239"><mml:mi mathvariant="fraktur">g</mml:mi></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si12.svg" display="inline" id="d1e246"><mml:mo>⊃</mml:mo></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si315.svg" display="inline" id="d1e251"><mml:mi mathvariant="fraktur">g</mml:mi></mml:math> <mml:math

Campoamor-Stursberg, Rutwig; Latini, Danilo; Marquette, Ian; Zhang, Yao-Zhong

doi:10.1016/j.aop.2023.169496

Annals of Physics

2023

DOI: 10.1016/j.aop.2023.169496

|View full text |Cite

Polynomial algebras from Lie algebra reduction chains g ⊃ g

Rutwig Campoamor-Stursberg,

Danilo Latini,

Ian Marquette

et al.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

Publication Types

Select...

Article1

Relationship

Self Cite1

Independent0

Authors

Journals

Cited by 1 publication

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

On polynomial symmetry algebras underlying superintegrable systems in Darboux spaces

Marquette,

Zhang,

Zhang

2023

J. Phys.: Conf. Ser.

Self Cite

View full text Add to dashboard Cite

We review three different approaches to polynomial symmetry algebras underlying superintegrable systems in Darboux spaces. The first method consists of using deformed oscillator algebra to obtain finite-dimensional representations of quadratic algebras. This allow one to gain information on the spectrum of the superintegrable systems. The second method has similarities with the induced module construction approach in the context of Lie algebras and can be used to construct infinite dimensional representations of the symmetry algebras. Explicit construction of these representations is a non-trivial task due to the non-linearity of the polynomial algebras. This method allows the construction of states of the superintegrable systems beyond the reach of separation of variables. As a result, we are able to construct a large number of states in terms of Airy, Bessel and Whittaker functions which would be difficult to obtain in other ways. We also discuss the third approach which is based on the notion of commutants of subalgebras in the enveloping algebra of a Poisson algebra or a Lie algebra. This allows us to discover new superintegrable models in the Darboux spaces and to construct their integrals and symmetry algebras via polynomials in the enveloping algebras.

show abstract

On polynomial symmetry algebras underlying superintegrable systems in Darboux spaces

Marquette,

Zhang,

Zhang

2023

J. Phys.: Conf. Ser.

Self Cite

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Polynomial algebras from Lie algebra reduction chains g ⊃ g

Cited by 1 publication

References 45 publications

On polynomial symmetry algebras underlying superintegrable systems in Darboux spaces

On polynomial symmetry algebras underlying superintegrable systems in Darboux spaces

Contact Info

Product

Resources

About