The universal central extension of the three-point 𝔰𝔩₂ loop algebra

Benkart, Georgia; Terwilliger, Paul

doi:10.1090/S0002-9939-07-08765-5

The universal central extension of the three-point $\mathfrak {sl}_2$ loop algebra
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by Georgia Benkart and Paul Terwilliger PDF

Proc. Amer. Math. Soc. 135 (2007), 1659-1668 Request permission

Abstract:

We consider the three-point loop algebra, \[ L= \mathfrak {sl}_2\otimes \mathbb {K} \lbrack t, t^{-1}, (t-1)^{-1}\rbrack ,\] where $\mathbb {K}$ denotes a field of characteristic $0$ and $t$ is an indeterminate. The universal central extension $\widehat L$ of $L$ was determined by Bremner. In this note, we give a presentation for $\widehat L$ via generators and relations, which highlights a certain symmetry over the alternating group $A_4$. To obtain our presentation of $\widehat L$, we use the realization of $L$ as the tetrahedron Lie algebra.

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