Realizations of the three point algebra $\mathfrak{sl}(2,\mathcal{R})\oplus \left({\Omega }_{\mathcal{R}}/d\mathcal{R}\right)$

Abstract

We describe the universal central extension of the three point current algebra $\mathfrak{sl}(2,\mathcal{R})$ where $\mathcal{R}=\mathbb{C}[t,t^{-1},u|u^2=t^2+4t]$ and construct realizations of it in terms of sums of partial differential operators.

arXiv admin note: text overlap with arXiv:0902.1273. This version has a correction to a scalar in Cor 2.3. The representations of the algebra are unaffected

References in corpus (1)

• Global Geometric Deformations of the Virasoro algebra, current and affine algebras by Krichever-Novikov type algebra

Cited by in corpus (3)

• The 3-point Virasoro algebra and its action on a Fock space
• Superelliptic Affine Lie algebras and orthogonal polynomials
• On the universal central extension of superelliptic affine Lie algebras