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 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 Isomorphic exponential Weyl algebras

1991 ◽  
Vol 33 (1) ◽  
pp. 7-10 ◽  
Author(s):  
P. L. Robinson
Keyword(s):  
Vector Space ◽  
Weyl Algebra ◽  
Associative Algebras ◽  
Exponential Form ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Weyl Algebras ◽  
The Subject ◽  
Symplectic Vector Space

Canonically associated to a real symplectic vector space are several associative algebras. The Weyl algebra (generated by the Heisenberg commutation relations) has been the subject of much study; see [1] for example. The exponential Weyl algebra (generated by the canonical commutation relations in exponential form) has been less well studied; see [8].

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

CLASSICAL LIE SUPERALGEBRAS OVER SIMPLE ASSOCIATIVE ALGEBRAS

2006 ◽  
Vol 92 (3) ◽  
pp. 581-600 ◽  
Author(s):  
GEORGIA BENKART ◽  
XIAOPING XU ◽  
KAIMING ZHAO
Keyword(s):  
Lie Algebras ◽  
Associative Algebra ◽  
Weyl Algebra ◽  
Identity Element ◽  
Lie Superalgebras ◽  
Associative Algebras ◽  
Matrix Algebras ◽  
Weyl Algebras ◽  
Conformal Algebras ◽  
The Matrix

Over arbitrary fields of characteristic not equal to 2, we construct three families of simple Lie algebras and six families of simple Lie superalgebras of matrices with entries chosen from different one-sided ideals of a simple associative algebra. These families correspond to the classical Lie algebras and superalgebras. Our constructions intermix the structure of the associative algebra and the structure of the matrix algebra in an essential, compatible way. Many examples of simple associative algebras without an identity element arise as a by-product. The study of conformal algebras and superalgebras often involves matrix algebras over associative algebras such as Weyl algebras, and for that reason, we illustrate our constructions by taking various one-sided ideals from a Weyl algebra or a quantum torus.

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

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].

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