scholarly journals The generalized Weyl Poisson algebras and their Poisson simplicity criterion

2019 ◽  
Vol 110 (1) ◽  
pp. 105-119
Author(s):  
V. V. Bavula
Keyword(s):  
Large Class ◽  
Poisson Structure ◽  
Poisson Algebra ◽  
Explicit Description ◽  
Poisson Algebras ◽  
Weyl Algebras ◽  
Generalized Weyl Algebras

Abstract A new large class of Poisson algebras, the class of generalized Weyl Poisson algebras, is introduced. It can be seen as Poisson algebra analogue of generalized Weyl algebras or as giving a Poisson structure to (certain) generalized Weyl algebras. A Poisson simplicity criterion is given for generalized Weyl Poisson algebras, and an explicit description of the Poisson centre is obtained. Many examples are considered (e.g. the classical polynomial Poisson algebra in 2n variables is a generalized Weyl Poisson algebra).

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 Quantization of a Poisson algebra and polynomials associated to links

1990 ◽  
Vol 120 ◽  
pp. 113-127 ◽  
Author(s):  
Tetsuya Ozawa
Keyword(s):  
Riemann Surface ◽  
Lie Algebra ◽  
Poisson Algebra ◽  
Homotopy Classes ◽  
Poisson Algebras

A formal quantization of Poisson algebras was discussed by several authors (see for instance Drinfel’d [D]). A formal Lie algebra generated by homotopy classes of loops on a Riemann surface ∑ was obtained by W. Goldman in [G], and its Poisson algebra was quantized, in the sense of Drinfel’d, by Turaev in [T].

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.

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].

scholarly journals Universal enveloping Hom-algebras of regular Hom-Poisson algebras

2022 ◽  
Vol 7 (4) ◽  
pp. 5712-5727
Author(s):  
Xianguo Hu ◽  
Keyword(s):  
Poisson Algebra ◽  
Poisson Algebras

<abstract><p>In this paper, we introduce universal enveloping Hom-algebras of Hom-Poisson algebras. Some properties of universal enveloping Hom-algebras of regular Hom-Poisson algebras are discussed. Furthermore, in the involutive case, it is proved that the category of involutive Hom-Poisson modules over an involutive Hom-Poisson algebra $ A $ is equivalent to the category of involutive Hom-associative modules over its universal enveloping Hom-algebra $ U_{eh}(A) $.</p></abstract>

scholarly journals Hochschild homology and cohomology of Generalized Weyl algebras: the quantum case

2013 ◽  
Vol 63 (3) ◽  
pp. 923-956 ◽  
Author(s):  
Andrea Solotar ◽  
Mariano Suárez-Alvarez ◽  
Quimey Vivas
Keyword(s):  
Hochschild Homology ◽  
Quantum Case ◽  
Weyl Algebras ◽  
Generalized Weyl Algebras
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