Bosonic realization of toroidal Lie algebras of classical types
Authors:
Naihuan Jing, Kailash C. Misra and Chongbin Xu
Journal:
Proc. Amer. Math. Soc. 137 (2009), 36093618
MSC (2000):
Primary 17B60, 17B67, 17B69; Secondary 17A45, 81R10
Published electronically:
June 10, 2009
MathSciNet review:
2529867
Fulltext PDF
Abstract 
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Additional Information
Abstract: Generalizing Feingold and Frenkel's construction, we use Weyl bosonic fields to construct toroidal Lie algebras of types , and of levels and respectively. In particular, our construction also gives new bosonic constructions for orthogonal Lie algebras in the cases of affine Lie algebras.
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 Y. Billig, Principal vertex operator representations for toroidal Lie algebras. J. Math. Phys. 39 (1998), no. 7, 38443864. MR 1630546 (99j:17041)
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 A. Feingold, I. B. Frenkel, Classical affine algebras. Adv. Math. 56 (1985), 117172. MR 788937 (87d:17018)
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 I. Frenkel, N. Jing, W. Wang, Vertex representations via finite groups and the McKay correspondence. Int. Math. Res. Notices 4 (2000), 195222. MR 1747618 (2001c:17042)
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 Y. Gao, Fermionic and bosonic representations of the extended affine Lie algebra . Canad. Math. Bull. 45 (2002), no. 4, 623633. MR 1941230 (2003h:17030)
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 C. Jiang, D. Meng, Vertex representations for the toroidal Lie algebra of type . J. Algebra 246 (2001), no. 2, 564593. MR 1872115 (2003b:17036)
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Additional Information
Naihuan Jing
Affiliation:
School of Sciences, South China University of Technology, Guangzhou 510640, People’s Republic of China – and – Department of Mathematics, North Carolina State University, Raleigh, North Carolina 276958205
Email:
jing@math.ncsu.edu
Kailash C. Misra
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, North Carolina 276958205
Email:
misra@math.ncsu.edu
Chongbin Xu
Affiliation:
School of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, People’s Republic of China
Email:
xuchongbin1977@126.com
DOI:
http://dx.doi.org/10.1090/S0002993909099420
PII:
S 00029939(09)099420
Keywords:
Toroidal algebras,
Weyl algebras,
vertex operators,
representations
Received by editor(s):
November 19, 2008
Received by editor(s) in revised form:
February 23, 2009
Published electronically:
June 10, 2009
Additional Notes:
The first author was supported by NSA grant H982300610083 and NSFC grant 10728102, and the second author was supported by NSA grant H98230080080.
Communicated by:
Gail R. Letzter
Article copyright:
© Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
