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Bosonic realization of toroidal Lie algebras of classical types
Author(s):
Naihuan
Jing;
Kailash
C.
Misra;
Chongbin
Xu
Journal:
Proc. Amer. Math. Soc.
137
(2009),
3609-3618.
MSC (2000):
Primary 17B60, 17B67, 17B69;
Secondary 17A45, 81R10
Posted:
June 10, 2009
MathSciNet review:
2529867
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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.
References:
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- [B]
- Y. Billig, Principal vertex operator representations for toroidal Lie algebras. J. Math. Phys. 39 (1998), no. 7, 3844-3864. MR 1630546 (99j:17041)
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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 27695-8205
Email:
jing@math.ncsu.edu
Kailash
C.
Misra
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205
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:
10.1090/S0002-9939-09-09942-0
PII:
S 0002-9939(09)09942-0
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
Posted:
June 10, 2009
Additional Notes:
The first author was supported by NSA grant H98230-06-1-0083 and NSFC grant 10728102, and the second author was supported by NSA grant H98230-08-0080.
Communicated by:
Gail R. Letzter
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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