Four-point affine Lie algebras
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- by Murray Bremner
- Proc. Amer. Math. Soc. 123 (1995), 1981-1989
- DOI: https://doi.org/10.1090/S0002-9939-1995-1249871-8
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Abstract:
We consider Lie algebras of the form $\mathfrak {g} \otimes R$ where $\mathfrak {g}$ is a simple complex Lie algebra and $R = \mathbb {C}[s,{s^{ - 1}},{(s - 1)^{ - 1}},{(s - a)^{ - 1}}]$ for $a \in \mathbb {C} - \{ 0,1\}$. After showing that R is isomorphic to a quadratic extension of the ring $\mathbb {C}[t,{t^{ - 1}}]$ of Laurent polynomials, we prove that $g \otimes R$ is a quasi-graded Lie algebra with a triangular decomposition. We determine the universal central extension of $\mathfrak {g} \otimes R$ and show that the cocycles defining it are closely related to ultraspherical (Gegenbauer) polynomials.References
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Bibliographic Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 1981-1989
- MSC: Primary 17B67; Secondary 33C45, 33C50
- DOI: https://doi.org/10.1090/S0002-9939-1995-1249871-8
- MathSciNet review: 1249871