The alternating central extension of the Onsager Lie algebra

2021/04/16 by Terwilliger, Paul
#17B37 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2104.08106

Abstract

The Onsager Lie algebra O is often used to study integrable lattice models. The universal enveloping algebra of O admits a q-deformation O_q called the q-Onsager algebra. Recently, an algebra \mathcal O_q was introduced called the alternating central extension of O_q. In this paper we introduce a Lie algebra \mathcal O that is roughly described by the following two analogies: (i) \mathcal O is to O as \mathcal O_q is to O_q; (ii) O_q is to O as \mathcal O_q is to \mathcal O. We call \mathcal O the alternating central extension of O. This paper contains a comprehensive description of \mathcal O.

Related

• The compact presentation for the alternating central extension of the q-Onsager algebra
• The Onsager Algebra
• The q-Onsager algebra
• The alternating central extension for the positive part of U_q(\widehat\mathfraksl₂)
• The q-Onsager Algebra and the Quantum Torus