
TL;DR
This paper introduces the universal Askey-Wilson algebra, a central extension of the original algebra, and explores its structure, automorphisms, and relations to other algebraic objects.
Contribution
It defines the universal Askey-Wilson algebra, provides a basis, describes its center, and establishes a faithful action of the modular group.
Findings
Introduces the universal Askey-Wilson algebra as a central extension.
Provides a linear basis for the algebra.
Describes the algebra's center and automorphism group.
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 of AW, obtained from AW by reinterpreting certain parameters as central elements in the algebra. We call the {\it universal Askey-Wilson algebra}. We give a faithful action of the modular group on as a group of automorphisms. We give a linear basis for . We describe the center of and the 2-sided ideal . We discuss how is related to the -Onsager algebra.
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