A Reduction Theorem for Highest Weight Modules over Toroidal Lie Algebras

2004 ◽  
Vol 250 (1) ◽  
pp. 47-63 ◽  
Author(s):  
Ivan Dimitrov ◽  
Vyacheslav Futorny ◽  
Ivan Penkov
Keyword(s):  
Lie Algebras ◽  
Reduction Theorem ◽  
Highest Weight ◽  
Highest Weight Modules ◽  
Weight Modules

Categories of nonstandard highest weight modules for affine Lie algebras

1996 ◽  
Vol 221 (1) ◽  
pp. 193-209 ◽  
Author(s):  
B. Cox ◽  
V. Futorny ◽  
D. Melville
Keyword(s):  
Lie Algebras ◽  
Affine Lie Algebras ◽  
Highest Weight ◽  
Highest Weight Modules ◽  
Weight Modules

scholarly journals Classification of irreducible integrable highest weight modules for current Kac–Moody algebras

2016 ◽  
Vol 16 (07) ◽  
pp. 1750123 ◽  
Author(s):  
S. Eswara Rao ◽  
Punita Batra
Keyword(s):  
Lie Algebras ◽  
Direct Sums ◽  
Highest Weight ◽  
Finite Dimensional ◽  
Highest Weight Modules ◽  
Weight Modules

This paper classifies irreducible, integrable highest weight modules for “current Kac–Moody Algebras” with finite-dimensional weight spaces. We prove that these modules turn out to be modules of appropriate direct sums of finitely many copies of Kac–Moody Lie algebras.

Categories of nonstandard highest weight modules for affine Lie algebras

1996 ◽  
Vol 221 (2) ◽  
pp. 193-209 ◽  
Author(s):  
B. Cox ◽  
V. Futorny ◽  
D. Melville
Keyword(s):  
Lie Algebras ◽  
Affine Lie Algebras ◽  
Highest Weight ◽  
Highest Weight Modules ◽  
Weight Modules
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