Weight modules for Weyl algebras

2004 ◽  
pp. 17-42 ◽  
Author(s):  
Viktor Bekkert ◽  
Georgia Benkart ◽  
Vyacheslav Futorny
Keyword(s):  
Weyl Algebras ◽  
Weight Modules

scholarly journals Simple weight modules over weak generalized Weyl algebras

2015 ◽  
Vol 219 (8) ◽  
pp. 3427-3444 ◽  
Author(s):  
Rencai Lü ◽  
Volodymyr Mazorchuk ◽  
Kaiming Zhao
Keyword(s):  
Weyl Algebras ◽  
Generalized Weyl Algebras ◽  
Weight Modules

Some associative algebras related to $U(\mathfrak g)$ and twisted generalized Weyl algebras

2003 ◽  
Vol 92 (1) ◽  
pp. 5 ◽  
Author(s):  
V. Mazorchuk ◽  
M. Ponomarenko ◽  
L. Turowska
Keyword(s):  
Weyl Algebra ◽  
Associative Algebras ◽  
Graded Modules ◽  
Weyl Algebras ◽  
Generalized Weyl Algebra ◽  
Generalized Weyl Algebras ◽  
Weight Modules

We prove that both Mickelsson step algebras and Orthogonal Gelfand-Zetlin algebras are twisted generalized Weyl algebras. Using an analogue of the Shapovalov form we construct all weight simple graded modules and some classes of simple weight modules over a twisted generalized Weyl algebra, improving the results from [6], where a particular class of algebras was considered and only special modules were classified.

scholarly journals Weight Modules over Generalized Weyl Algebras

1996 ◽  
Vol 184 (2) ◽  
pp. 491-504 ◽  
Author(s):  
Yuri A. Drozd ◽  
Boris L. Guzner ◽  
Sergei A. Ovsienko
Keyword(s):  
Weyl Algebras ◽  
Generalized Weyl Algebras ◽  
Weight Modules

scholarly journals Weight modules over infinite dimensional Weyl algebras

2014 ◽  
Vol 142 (9) ◽  
pp. 3049-3057 ◽  
Author(s):  
Vyacheslav Futorny ◽  
Dimitar Grantcharov ◽  
Volodymyr Mazorchuk
Keyword(s):  
Infinite Dimensional ◽  
Weyl Algebras ◽  
Weight Modules

Weight modules of quantum Weyl algebras

2020 ◽  
Vol 27 (6) ◽  
pp. 1707-1753
Author(s):  
Vyacheslav Futorny ◽  
Laurent Rigal ◽  
Andrea Solotar
Keyword(s):  
Weyl Algebras ◽  
Weight Modules
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