Quasifinite highest weight modules over the Lie algebra of matrix differential operators on the circle

1998 ◽  
Vol 39 (5) ◽  
pp. 2910-2928 ◽  
Author(s):  
Carina Boyallian ◽  
Victor G. Kac ◽  
José I. Liberati ◽  
Catherine H. Yan
Keyword(s):  
Lie Algebra ◽  
Differential Operators ◽  
Highest Weight ◽  
Matrix Differential Operators ◽  
Highest Weight Modules ◽  
Matrix Differential ◽  
Weight Modules

scholarly journals Representations of the Twisted Heisenberg–Virasoro Algebra at Level Zero

2003 ◽  
Vol 46 (4) ◽  
pp. 529-537 ◽  
Author(s):  
Yuly Billig
Keyword(s):  
Lie Algebra ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Highest Weight ◽  
Level Zero ◽  
Maximal Submodule ◽  
Highest Weight Modules ◽  
Weight Modules

AbstractWe describe the structure of the irreducible highest weight modules for the twisted Heisenberg–Virasoro Lie algebra at level zero. We prove that either a Verma module is irreducible or its maximal submodule is cyclic.

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