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On the universal central extension of hyperelliptic current algebras


Author: Ben Cox
Journal: Proc. Amer. Math. Soc. 144 (2016), 2825-2835
MSC (2010): Primary 17B37, 17B67; Secondary 81R10
DOI: https://doi.org/10.1090/proc/13057
Published electronically: March 1, 2016
MathSciNet review: 3487217
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Abstract: Let $ p(t)\in \mathbb{C}[t]$ be a polynomial with distinct roots and nonzero constant term. We describe, using Faà de Bruno's formula and Bell polynomials, the universal central extension in terms of generators and relations for the hyperelliptic current Lie algebras $ \mathfrak{g}\otimes R$ whose coordinate ring is of the form $ R=\mathbb{C}[t,t^{-1},u\,\vert\, u^2=p(t)]$.


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Additional Information

Ben Cox
Affiliation: Department of Mathematics, University of Charleston, 66 George Street, Charleston, South Carolina 29424
Email: coxbl@cofc.edu

DOI: https://doi.org/10.1090/proc/13057
Keywords: Universal central extensions, Krichever-Novikov algebras, hyperelliptic current algebras
Received by editor(s): March 12, 2015
Received by editor(s) in revised form: September 3, 2015
Published electronically: March 1, 2016
Additional Notes: Travel to the Mittag-Leffler Institute was partially supported by a Simons Collaborations Grant.
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2016 American Mathematical Society