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Beyond Borcherds Lie algebras and inside
Author(s):
Stephen
Berman;
Elizabeth
Jurisich;
Shaobin
Tan
Journal:
Trans. Amer. Math. Soc.
353
(2001),
1183-1219.
MSC (2000):
Primary 17B65;
Secondary 17B69
Posted:
November 8, 2000
MathSciNet review:
1707191
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Abstract:
We give a definition for a new class of Lie algebras by generators and relations which simultaneously generalize the Borcherds Lie algebras and the Slodowy G.I.M. Lie algebras. After proving these algebras are always subalgebras of Borcherds Lie algebras, as well as some other basic properties, we give a vertex operator representation for a factor of them. We need to develop a highly non-trivial generalization of the square length two cut off theorem of Goddard and Olive to do this.
References:
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- [BM]
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- [Bo3]
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- [EMY]
- S. Eswara Rao, R.V. Moody and T. Yokonuma, Lie algebras and Weyl groups arising from vertex operator representations, Nova J. of Algebra and Geometry, 1(1992), 15-57. MR 93h:17040
- [FLM]
- I.B. Frenkel, J. Lepowsky and A. Meurman, Vertex operator algebras and the Monster, Academic Press, Boston, 1988. MR 90h:17026
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- [J2]
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Additional Information:
Stephen
Berman
Affiliation:
Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, Saskatchewan, S7N 5E6 Canada
Email:
berman@snoopy.usask.ca
Elizabeth
Jurisich
Affiliation:
Department of Mathematics, University of California, Santa Cruz, California 95064
Address at time of publication:
Department of Mathematics, College of Charleston, Charleston, South Carolina 29424
Email:
jurisiche@cofc.edu
Shaobin
Tan
Affiliation:
Department of Mathematics, Xiamen University, Xiamen, 361005 Fujian, People's Republic of China
Email:
tans@jingxian.xmu.edu.cn
DOI:
10.1090/S0002-9947-00-02582-4
PII:
S 0002-9947(00)02582-4
Received by editor(s):
March 18, 1998
Received by editor(s) in revised form:
May 7, 1999
Posted:
November 8, 2000
Additional Notes:
The first auther gratefully acknowledges the support of the Natural Sciences and Engineering Research Council of Canada
Dedicated:
This paper is dedicated to Professor Peter Slodowy
Copyright of article:
Copyright
2000,
American Mathematical Society
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