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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Beyond Borcherds Lie algebras and inside
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by Stephen Berman, Elizabeth Jurisich and Shaobin Tan PDF
Trans. Amer. Math. Soc. 353 (2001), 1183-1219 Request permission


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:
  • 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:
  • Shaobin Tan
  • Affiliation: Department of Mathematics, Xiamen University, Xiamen, 361005 Fujian, People’s Republic of China
  • Email:
  • 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
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 1183-1219
  • MSC (2000): Primary 17B65; Secondary 17B69
  • DOI:
  • MathSciNet review: 1707191