The Universal Askey-Wilson Algebra

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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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dc.contributor.author	Terwilliger, P.
dc.date.accessioned	2019-02-14T16:59:45Z
dc.date.available	2019-02-14T16:59:45Z
dc.date.issued	2011
dc.identifier.citation	The Universal Askey-Wilson Algebra / P. Terwilliger // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 66 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 33D80; 33D45
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/147390
dc.description.abstract	In 1992 A. Zhedanov introduced the Askey-Wilson algebra AW=AW(3) and used it to describe the Askey-Wilson polynomials. In this paper we introduce a central extension Δ of AW, obtained from AW by reinterpreting certain parameters as central elements in the algebra. We call Δ the universal Askey-Wilson algebra. We give a faithful action of the modular group PSL₂(Z) on Δ as a group of automorphisms. We give a linear basis for Δ. We describe the center of Δ and the 2-sided ideal Δ[Δ,Δ]Δ. We discuss how Δ is related to the q-Onsager algebra.	uk_UA
dc.description.sponsorship	This paper is a contribution to the Special Issue “Relationship of Orthogonal Polynomials and Special Functions with Quantum Groups and Integrable Systems”. The full collection is available a thttp://www.emis.de/journals/SIGMA/OPSF.html.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	The Universal Askey-Wilson Algebra	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA
dc.identifier.udc	DOI:10.3842/SIGMA.2011.069