The Universal Central Extension of the Three-point sl₂ Loop Algebra

We give a presentation of the universal central extension of the three-point loop algebra L over sl_2 by generators and relations. Our presentation arises from the realization of L as the tetrahedron Lie algebra and leads to connections between the universal central extension and the Onsager Lie algebra. Symmetry under the alternating group A_4 features prominently in this work.