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Transactions of the American Mathematical Society

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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
Published electronically: November 8, 2000
MathSciNet review: 1707191
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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

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

Shaobin Tan
Affiliation: Department of Mathematics, Xiamen University, Xiamen, 361005 Fujian, People’s Republic of China

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