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DJKM algebras I: Their universal central extension

Authors: Ben Cox and Vyacheslav Futorny
Journal: Proc. Amer. Math. Soc. 139 (2011), 3451-3460
MSC (2010): Primary 17B65, 17B67; Secondary 81R10
Published electronically: March 9, 2011
MathSciNet review: 2813377
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Abstract: The purpose of this paper is to explicitly describe in terms of generators and relations the universal central extension of the infinite dimensional Lie algebra, $ \mathfrak{g}\otimes \mathbb{C}[t,t^{-1},u\vert u^2=(t^2-b^2)(t^2-c^2)]$, appearing in the work of Date, Jimbo, Kashiwara and Miwa in their study of integrable systems arising from the Landau-Lifshitz differential equation.

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Additional Information

Ben Cox
Affiliation: Department of Mathematics, College of Charleston, 66 George Street, Charleston, South Carolina 29424

Vyacheslav Futorny
Affiliation: Department of Mathematics, University of São Paulo, São Paulo, Brazil

Keywords: Krichever-Novikov algebras, Landau-Lifshitz differential equation, Date-Jimbo-Miwa-Kashiwara algebras, universal central extension, ultraspherical polynomials, elliptic integrals
Received by editor(s): September 5, 2010
Published electronically: March 9, 2011
Additional Notes: The first author is grateful to the Fapesp (processo 2009/17533-6) and the University of São Paulo for their support and hospitality during his visit to São Paulo. The first author was also partially supported by a research and development grant from the College of Charleston.
The second author was partially supported by Fapesp (processo 2005/60337-2) and CNPq (processo 301743/2007-0).
Communicated by: Gail R. Letzter
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.