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 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 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.

scholarly journals ORE AND GOLDIE THEOREMS FOR SKEW PBW EXTENSIONS

2013 ◽  
Vol 06 (04) ◽  
pp. 1350061 ◽  
Author(s):  
Oswaldo Lezama ◽  
Juan Pablo Acosta ◽  
Cristian Chaparro ◽  
Ingrid Ojeda ◽  
César Venegas
Keyword(s):  
Commutative Rings ◽  
Polynomial Rings ◽  
Quantum Matrices ◽  
Weyl Algebras ◽  
Skew Polynomial Rings ◽  
Finite Dimensional ◽  
Quantum Version ◽  
Skew Pbw Extensions ◽  
Skew Polynomial ◽  
Finite Dimensional Lie Algebras

Many rings and algebras arising in quantum mechanics can be interpreted as skew Poincaré–Birkhoff–Witt (PBW) extensions. Indeed, Weyl algebras, enveloping algebras of finite-dimensional Lie algebras (and its quantization), Artamonov quantum polynomials, diffusion algebras, Manin algebra of quantum matrices, among many others, are examples of skew PBW extensions. In this paper, we extend the classical Ore and Goldie theorems, known for skew polynomial rings, to this wide class of non-commutative rings. As application, we prove the quantum version of the Gelfand–Kirillov conjecture for the skew quantum polynomials.

scholarly journals Holonomic modules for rings of invariant differential operators

2021 ◽  
pp. 1-18
Author(s):  
Vyacheslav Futorny ◽  
João Schwarz
Keyword(s):  
Differential Operators ◽  
Main Tool ◽  
Bernstein Inequality ◽  
Invariant Differential Operators ◽  
Weyl Algebras ◽  
Invariant Differential ◽  
Quotient Varieties ◽  
Generalized Weyl Algebras ◽  
A Finite Group ◽  
Holonomic Modules

We study holonomic modules for the rings of invariant differential operators on affine commutative domains with finite Krull dimension with respect to arbitrary actions of finite groups. We prove the Bernstein inequality for these rings. Our main tool is the filter dimension introduced by Bavula. We extend the results for the invariants of the Weyl algebra with respect to the symplectic action of a finite group, for the rings of invariant differential operators on quotient varieties, and invariants of certain generalized Weyl algebras under the linear actions. We show that the filter dimension of all above mentioned algebras equals [Formula: see text].

Sign in / Sign up

Export Citation Format

Share Document