RESEARCH ARTICLE

Twisted fermionic and bosonic representations for a class of BC-graded Lie algebras

  • Fulin CHEN ,
  • Shaobin TAN
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  • School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

Received date: 28 Mar 2011

Accepted date: 15 Dec 2015

Published date: 01 Aug 2011

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

In this paper, we study the fermionic and bosonic representations for a class of BC-graded Lie algebras coordinatized by skew Laurent polynomial rings. This generalizes the fermionic and bosonic constructions for the affine Kac-Moody algebras of type AN(2).

Cite this article

Fulin CHEN , Shaobin TAN . Twisted fermionic and bosonic representations for a class of BC-graded Lie algebras[J]. Frontiers of Mathematics in China, 2011 , 6(4) : 607 -628 . DOI: 10.1007/s11464-011-0147-4

1
Allison B N, Azam S, Berman S, Gao Y, Pianzola A. Extended Affine Lie Algebras and Their Root Systems. Mem Amer Math Soc, Vol 126, No 603. Providence: Am Math Soc, 1997

2
Allison B N, Benkart G, Gao Y. Central extensions of Lie algebras graded by finite root systems. Math Ann, 2000, 316: 499-527

DOI

3
Allison B N, Benkart G, Gao Y. Lie Algebras Graded by the Root Systems BCr, r≥2. Mem Am Math Soc, Vol 158, No 751. Providence: Am Math Soc, 2002

4
Benkart G, Zelmanov E. Lie algebras graded by finite root systems and intersection matrix algebras. Invent Math, 1996, 126: 1-45

DOI

5
Berman S, Moody R V. Lie algebras graded by finite root systems and the intersection matrix algebras of Slodowy. Invent Math, 1992, 108: 323-347

DOI

6
Chen H, Gao Y. BCN-graded Lie algebras arising from fermionic representations. J Alg, 2007, 308: 545-566

DOI

7
Feingold A J, Frenkel I B. Classical affine Lie algebras. Adv Math, 1985, 56: 117-172

DOI

8
Frenkel I B. Spinor representation of affine Lie algebras. Proc Natl Acad Sci USA, 1980, 77: 6303-6306

DOI

9
Frenkel I B. Two constructions of affine Lie algebra representations and boson-fermion correspondence in quantum field theory. J Funct Anal, 1981, 44: 259-327

DOI

10
Gao Y. Vertex operators arising from the homogeneous realization for g^lN. Comm Math Phys, 2000, 211: 23-66

DOI

11
Gao Y. Fermionic and bosonic representations of the extended affine Lie algebra glN(ℂq) ˜. Canada Math Bull, 2002, 45: 623-633

DOI

12
Jing N, Misra K C. Fermionic realization of toroidal Lie algebras of classical types. J Alg, 2010, 324: 183-194

DOI

13
Jing N, Misra K C, Xu C. Bosonic realization of toroidal Lie algebras of classical types. Proc Am Math Soc, 2009, 137: 3609-3618

DOI

14
Kac V G, Peterson D H. Spin and wedge representations of infinite-dimensional Lie algebras and groups. Proc Natl Acad Sci USA, 1981, 78: 3308-3312

DOI

15
Lau M. Bosonic and fermionic representations of Lie algebra central extensions. Adv Math, 2005, 194: 225-245

DOI

16
Neher E. Lie algebras graded by 3-graded root systems. Am J Math, 1996, 118: 439-491

DOI

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