Isomorphisms Between Quantum Generalized Weyl Algebras

Richard, Lionel; Solotar, Andréa

doi:10.1142/s0219498806001685

Cited by 35 publications

(37 citation statements)

References 16 publications

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“…Other generalized Weyl algebras of the form K[X](X σ → qX, a), with q not a root of unity, were studied in [23], and their automorphism group was determined. With minor changes, [23,Cor. 2.2.7] can be adapted to describe the automorphism group of the down-up algebras of the form A(r + 1, −r, 0), with r ∈ K * not a root of unity.…”

Section: Some Well-known Examplesmentioning

confidence: 99%

Automorphisms of Generalized Down-Up Algebras

Carvalho

Lopes

2009

Communications in Algebra

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A generalization of down-up algebras was introduced by Cassidy and Shelton in [11], the so-called generalized down-up algebras. We describe the automorphism group of conformal Noetherian generalized down-up algebras L(f, r, s, γ) such that r is not a root of unity, listing explicitly the elements of the group. In the last section we apply these results to Noetherian down-up algebras, thus obtaining a characterization of the automorphism group of Noetherian down-up algebras A(α, β, γ) for which the roots of the polynomial X 2 − αX − β are not both roots of unity.

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Section: Some Well-known Examplesmentioning

confidence: 99%

Automorphisms of Generalized Down-Up Algebras

Carvalho

Lopes

2009

Communications in Algebra

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“…The algebra A q,Λ n (K) also fits into the class of generalized Wey algebras [4]. The isomorphism problem for some rank-one generalized Weyl algebras has been studied in [5,31]. In general, it would be interesting to determine the automorphism group for A q,Λ n (K) and obtain an isomorphism classification for the family {A q,Λ n (K)}.…”

Section: Introductionmentioning

confidence: 99%

Automorphisms for Some Symmetric Multiparameter Quantized Weyl Algebras and Their Localizations

Tang

2017

Algebra Colloq.

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We study a family of “symmetric” multiparameter quantized Weyl algebras [Formula: see text] and some related algebras. We compute the Nakayama automorphism of [Formula: see text], give a necessary and sufficient condition for [Formula: see text] to be Calabi-Yau, and prove that [Formula: see text] is cancellative. We study the automorphisms and isomorphism problem for [Formula: see text] and [Formula: see text]. Similar results are established for the Maltsiniotis multiparameter quantized Weyl algebra [Formula: see text] and its polynomial extension. We prove a quantum analogue of the Dixmier conjecture for a simple localization [Formula: see text] and determine its automorphism group.

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“…The problem of when two quantum generalized Weyl algebras are isomorphic was solved by Bavula and Jordan in [6] for q not a root of unity. The same problem when working over a polynomial ring was addressed by Richard and Solotar in [10].…”

Section: Introductionmentioning

confidence: 82%

Endomorphisms of quantum generalized Weyl algebras

Launois

2015

ACM Commun. Comput. Algebra

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We prove that every endomorphism of a simple quantum generalized Weyl algebra A over a commutative Laurent polynomial ring in one variable is an automorphism. This is achieved by obtaining an explicit classification of all endomorphisms of A. Our main result applies to minimal primitive factors of the quantized enveloping algebra of U q (sl 2 ) and certain minimal primitive quotients of the positive part of U q (so 5 ).2010 Mathematics subject classification: 16W35, 16S32, 16W20, 17B37

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Isomorphisms Between Quantum Generalized Weyl Algebras

Abstract: We study isomorphisms between generalized Weyl algebras, giving a complete answer to the quantum case of this problem for R = k[h].

Cited by 35 publications

References 16 publications

Automorphisms of Generalized Down-Up Algebras

Automorphisms of Generalized Down-Up Algebras

Automorphisms for Some Symmetric Multiparameter Quantized Weyl Algebras and Their Localizations

Endomorphisms of quantum generalized Weyl algebras

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