Realizations of the three-point Lie algebra $\mathfrak{sl}(2, \mathcal R) \oplus( \Omega_{\mathcal R}/d{\mathcal R})$

Ben Cox and Elizabeth Jurisich

Vol. 270 (2014), No. 1, 27–48

DOI: 10.2140/pjm.2014.270.27

Abstract

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

This paper is dedicated to Robert Wilson.

Keywords

three point algebras, Krichever–Novikov algebras, free field realizations, Wakimoto modules, affine Lie algebras, Fock spaces

Mathematical Subject Classification 2010

Primary: 17B67

Secondary: 81R10

Milestones

Received: 20 March 2013

Revised: 17 December 2013

Accepted: 21 December 2013

Published: 2 August 2014