Automorphisms for Some "symmetric" Multiparameter Quantized Weyl Algebras and Their Localizations
Xin Tang

TL;DR
This paper investigates automorphisms, isomorphisms, and structural properties of symmetric multiparameter quantized Weyl algebras and their localizations, including automorphism groups, Calabi-Yau conditions, and a quantum Dixmier conjecture analogue.
Contribution
It provides explicit automorphism groups, solves the isomorphism problem, and establishes a quantum analogue of the Dixmier conjecture for these algebras.
Findings
Computed Nakayama automorphism and Calabi-Yau conditions.
Determined automorphism groups for algebras and their extensions.
Proved a quantum analogue of the Dixmier conjecture.
Abstract
In this paper, we study the algebra automorphisms and isomorphisms for a family of "symmetric" multiparameter quantized Weyl algebras and some related algebras in the generic case. First, we compute the Nakayama automorphism for and give a necessary and sufficient condition for to be Calabi-Yau. We also prove that is cancellative. Then we determine the automorphism group for and its polynomial extension . As an application, we solve the isomorphism problem for and . Similar results will be established for the Maltisiniotis multiparameter quantized Weyl algebra and its polynomial extension . In addition, we prove a quantum analogue of the Dixmier conjecture for a simple localization of . Moreover, we will completely determine the algebra automorphism group for .
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry
