The Universal Central Extension of the Three-point sl_2 Loop Algebra

Georgia Benkart; Paul Terwilliger

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The Universal Central Extension of the Three-point sl_2 Loop Algebra

Georgia Benkart·Paul Terwilliger

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Abstract

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.

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Georgia Benkart, Paul Terwilliger. 2005-12-17. The Universal Central Extension of the Three-point sl_2 Loop Algebra. https://arxiv.org/abs/math/0512422

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