The alternating central extension of the Onsager Lie algebra

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 O q was introduced called the alternating central extension of O q . In this paper we introduce a Lie algebra O that is roughly described by the following two analogies:We call O the alternating central extension of O. This paper contains a comprehensive description of O.