scholarly journals Noncommutative Differential Geometry of Generalized Weyl Algebras

2016 ◽  
Author(s):  
Tomasz Brzeziński ◽  
Keyword(s):  
Differential Geometry ◽  
Weyl Algebras ◽  
Noncommutative Differential Geometry ◽  
Generalized Weyl Algebras

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

scholarly journals Generalized Weyl algebras and diskew polynomial rings

2019 ◽  
Vol 19 (10) ◽  
pp. 2050194
Author(s):  
V. V. Bavula
Keyword(s):  
Mild Condition ◽  
Polynomial Rings ◽  
Weyl Algebras ◽  
New Class ◽  
Generalized Weyl Algebras

The aim of the paper is to extend the class of generalized Weyl algebras (GWAs) to a larger class of rings (they are also called GWAs) that are determined by two ring endomorphisms rather than one as in the case of ‘old’ GWAs. A new class of rings, the diskew polynomial rings, is introduced that is closely related to GWAs (they are GWAs under a mild condition). Simplicity criteria are given for GWAs and diskew polynomial rings.

scholarly journals Fixed rings of quantum generalized Weyl algebras

2020 ◽  
Vol 48 (9) ◽  
pp. 4051-4064
Author(s):  
Jason Gaddis ◽  
Phuong Ho
Keyword(s):  
Weyl Algebras ◽  
Generalized Weyl Algebras

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.

Noncommutative differential geometry on the quantum SU(2), I: An algebraic viewpoint

K-Theory ◽  
1990 ◽  
Vol 4 (2) ◽  
pp. 157-180 ◽  
Author(s):  
Tetsuya Masuda ◽  
Yoshiomi Nakagami ◽  
Junsei Watanabe
Keyword(s):  
Differential Geometry ◽  
Noncommutative Differential Geometry
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