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Skew derivations on generalized Weyl algebras

Munerah Almulhem, Tomasz Brzeziński, Tomasz Brzezinski Orcid Logo

Journal of Algebra, Volume: 493, Pages: 194 - 235

Swansea University Author: Tomasz Brzezinski Orcid Logo

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DOI (Published version): 10.1016/j.jalgebra.2017.09.018

Abstract

A wide class of skew derivations on degree-one generalized Weyl algebras R(a, φ) over a ring R is constructed. All these derivations are twisted by a degree- counting extensions of automorphisms of R. It is determined which of the constructed derivations are Q-skew derivations. The compatibility of...

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Published in: Journal of Algebra
ISSN: 00218693
Published: 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa35456
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first_indexed 2017-09-20T19:09:17Z
last_indexed 2019-05-09T15:17:16Z
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spelling 2019-05-08T07:58:38.4688616 v2 35456 2017-09-20 Skew derivations on generalized Weyl algebras 30466d840b59627325596fbbb2c82754 0000-0001-6270-3439 Tomasz Brzezinski Tomasz Brzezinski true false 2017-09-20 SMA A wide class of skew derivations on degree-one generalized Weyl algebras R(a, φ) over a ring R is constructed. All these derivations are twisted by a degree- counting extensions of automorphisms of R. It is determined which of the constructed derivations are Q-skew derivations. The compatibility of these skew derivations with the natural Z-grading of R(a,φ) is studied. Additional classes of skew derivations are constructed for generalized Weyl algebras given by an automorphism φ of a finite order. Conditions that the central element a that forms part of the structure of R(a, φ) need to satisfy for the orthogonality of pairs of aforementioned skew derivations are derived. In addition local nilpotency of constructed derivations is studied. General constructions are illustrated by description of all skew derivations (twisted by a degree- counting extension of the identity automorphism) of generalized Weyl algebras over the polynomial ring in one variable and with a linear polynomial as the central element. Journal Article Journal of Algebra 493 194 235 00218693 1 1 2018 2018-01-01 10.1016/j.jalgebra.2017.09.018 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2019-05-08T07:58:38.4688616 2017-09-20T15:02:10.1212136 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Munerah Almulhem 1 Tomasz Brzeziński 2 Tomasz Brzezinski 0000-0001-6270-3439 3 0035456-20092017150350.pdf Weyl_derivation_complete_final.pdf 2017-09-20T15:03:50.9130000 Output 415932 application/pdf Accepted Manuscript true 2018-09-27T00:00:00.0000000 12 month embargo. true eng
title Skew derivations on generalized Weyl algebras
spellingShingle Skew derivations on generalized Weyl algebras
Tomasz Brzezinski
title_short Skew derivations on generalized Weyl algebras
title_full Skew derivations on generalized Weyl algebras
title_fullStr Skew derivations on generalized Weyl algebras
title_full_unstemmed Skew derivations on generalized Weyl algebras
title_sort Skew derivations on generalized Weyl algebras
author_id_str_mv 30466d840b59627325596fbbb2c82754
author_id_fullname_str_mv 30466d840b59627325596fbbb2c82754_***_Tomasz Brzezinski
author Tomasz Brzezinski
author2 Munerah Almulhem
Tomasz Brzeziński
Tomasz Brzezinski
format Journal article
container_title Journal of Algebra
container_volume 493
container_start_page 194
publishDate 2018
institution Swansea University
issn 00218693
doi_str_mv 10.1016/j.jalgebra.2017.09.018
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description A wide class of skew derivations on degree-one generalized Weyl algebras R(a, φ) over a ring R is constructed. All these derivations are twisted by a degree- counting extensions of automorphisms of R. It is determined which of the constructed derivations are Q-skew derivations. The compatibility of these skew derivations with the natural Z-grading of R(a,φ) is studied. Additional classes of skew derivations are constructed for generalized Weyl algebras given by an automorphism φ of a finite order. Conditions that the central element a that forms part of the structure of R(a, φ) need to satisfy for the orthogonality of pairs of aforementioned skew derivations are derived. In addition local nilpotency of constructed derivations is studied. General constructions are illustrated by description of all skew derivations (twisted by a degree- counting extension of the identity automorphism) of generalized Weyl algebras over the polynomial ring in one variable and with a linear polynomial as the central element.
published_date 2018-01-01T03:44:06Z
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score 11.035634

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