An Integral Basis for the Universal Enveloping Algebra of the Onsager Algebra

TL;DR

This paper develops an integral form and explicit basis for the universal enveloping algebra of the Onsager algebra, along with straightening identities to facilitate algebraic computations.

Contribution

It introduces the first explicit integral basis and straightening identities for the universal enveloping algebra of the Onsager algebra, advancing algebraic understanding.

Findings

Constructed an integral form for the algebra.

Provided an explicit integral basis.

Formulated straightening identities among basis elements.

Abstract

We construct an integral form for the universal enveloping algebra of the Onsager algebra and an explicit integral basis for this integral form. We also formulate straightening identities among some products of basis elements.