Beyond Borcherds Lie algebras and inside

Authors:
Stephen Berman, Elizabeth Jurisich and Shaobin Tan

Journal:
Trans. Amer. Math. Soc. **353** (2001), 1183-1219

MSC (2000):
Primary 17B65; Secondary 17B69

DOI:
https://doi.org/10.1090/S0002-9947-00-02582-4

Published electronically:
November 8, 2000

MathSciNet review:
1707191

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Abstract | References | Similar Articles | Additional Information

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.

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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:
https://doi.org/10.1090/S0002-9947-00-02582-4

Received by editor(s):
March 18, 1998

Received by editor(s) in revised form:
May 7, 1999

Published electronically:
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

Article copyright:
© Copyright 2000
American Mathematical Society