Journal
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 353, Issue 3, Pages 1183-1219Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/S0002-9947-00-02582-4
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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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