Pointed Hopf actions on quantum generalized Weyl algebras

We study actions of pointed Hopf algebras in the Z -graded setting. Our main result classifies inner-faithful actions of generalized Taft algebras on quantum generalized Weyl algebras which respect the Z -grading. We also show that gene...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Gaddis, Jason [verfasserIn] Won, Robert [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	Generalized Taft algebra Generalized Weyl algebra Hopf algebra actions

Übergeordnetes Werk:	Enthalten in: Journal of algebra - San Diego, Calif. : Elsevier, 1964, 601, Seite 312-331
Übergeordnetes Werk:	volume:601 ; pages:312-331

DOI / URN:	10.1016/j.jalgebra.2022.03.005

Katalog-ID:	ELV007660456

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520			\|a We study actions of pointed Hopf algebras in the Z -graded setting. Our main result classifies inner-faithful actions of generalized Taft algebras on quantum generalized Weyl algebras which respect the Z -grading. We also show that generically the invariant rings of Taft actions on quantum generalized Weyl algebras are commutative rings.
650		4	\|a Generalized Taft algebra
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650		4	\|a Hopf algebra actions
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spelling	10.1016/j.jalgebra.2022.03.005 doi (DE-627)ELV007660456 (ELSEVIER)S0021-8693(22)00094-1 DE-627 ger DE-627 rda eng 510 DE-600 31.20 bkl Gaddis, Jason verfasserin (orcid)0000-0003-2087-2829 aut Pointed Hopf actions on quantum generalized Weyl algebras 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study actions of pointed Hopf algebras in the Z -graded setting. Our main result classifies inner-faithful actions of generalized Taft algebras on quantum generalized Weyl algebras which respect the Z -grading. We also show that generically the invariant rings of Taft actions on quantum generalized Weyl algebras are commutative rings. Generalized Taft algebra Generalized Weyl algebra Hopf algebra actions Won, Robert verfasserin (orcid)0000-0002-9965-3196 aut Enthalten in Journal of algebra San Diego, Calif. : Elsevier, 1964 601, Seite 312-331 Online-Ressource (DE-627)266890423 (DE-600)1468947-9 (DE-576)10337311X 1090-266X nnns volume:601 pages:312-331 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines AR 601 312-331
allfields_unstemmed	10.1016/j.jalgebra.2022.03.005 doi (DE-627)ELV007660456 (ELSEVIER)S0021-8693(22)00094-1 DE-627 ger DE-627 rda eng 510 DE-600 31.20 bkl Gaddis, Jason verfasserin (orcid)0000-0003-2087-2829 aut Pointed Hopf actions on quantum generalized Weyl algebras 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study actions of pointed Hopf algebras in the Z -graded setting. Our main result classifies inner-faithful actions of generalized Taft algebras on quantum generalized Weyl algebras which respect the Z -grading. We also show that generically the invariant rings of Taft actions on quantum generalized Weyl algebras are commutative rings. Generalized Taft algebra Generalized Weyl algebra Hopf algebra actions Won, Robert verfasserin (orcid)0000-0002-9965-3196 aut Enthalten in Journal of algebra San Diego, Calif. : Elsevier, 1964 601, Seite 312-331 Online-Ressource (DE-627)266890423 (DE-600)1468947-9 (DE-576)10337311X 1090-266X nnns volume:601 pages:312-331 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines AR 601 312-331
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allfieldsSound	10.1016/j.jalgebra.2022.03.005 doi (DE-627)ELV007660456 (ELSEVIER)S0021-8693(22)00094-1 DE-627 ger DE-627 rda eng 510 DE-600 31.20 bkl Gaddis, Jason verfasserin (orcid)0000-0003-2087-2829 aut Pointed Hopf actions on quantum generalized Weyl algebras 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study actions of pointed Hopf algebras in the Z -graded setting. Our main result classifies inner-faithful actions of generalized Taft algebras on quantum generalized Weyl algebras which respect the Z -grading. We also show that generically the invariant rings of Taft actions on quantum generalized Weyl algebras are commutative rings. Generalized Taft algebra Generalized Weyl algebra Hopf algebra actions Won, Robert verfasserin (orcid)0000-0002-9965-3196 aut Enthalten in Journal of algebra San Diego, Calif. : Elsevier, 1964 601, Seite 312-331 Online-Ressource (DE-627)266890423 (DE-600)1468947-9 (DE-576)10337311X 1090-266X nnns volume:601 pages:312-331 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines AR 601 312-331
language	English
source	Enthalten in Journal of algebra 601, Seite 312-331 volume:601 pages:312-331
sourceStr	Enthalten in Journal of algebra 601, Seite 312-331 volume:601 pages:312-331
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authorswithroles_txt_mv	Gaddis, Jason @@aut@@ Won, Robert @@aut@@
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author	Gaddis, Jason
spellingShingle	Gaddis, Jason ddc 510 bkl 31.20 misc Generalized Taft algebra misc Generalized Weyl algebra misc Hopf algebra actions Pointed Hopf actions on quantum generalized Weyl algebras
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topic_title	510 DE-600 31.20 bkl Pointed Hopf actions on quantum generalized Weyl algebras Generalized Taft algebra Generalized Weyl algebra Hopf algebra actions
topic	ddc 510 bkl 31.20 misc Generalized Taft algebra misc Generalized Weyl algebra misc Hopf algebra actions
topic_unstemmed	ddc 510 bkl 31.20 misc Generalized Taft algebra misc Generalized Weyl algebra misc Hopf algebra actions
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title	Pointed Hopf actions on quantum generalized Weyl algebras
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title_full	Pointed Hopf actions on quantum generalized Weyl algebras
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title_sort	pointed hopf actions on quantum generalized weyl algebras
title_auth	Pointed Hopf actions on quantum generalized Weyl algebras
abstract	We study actions of pointed Hopf algebras in the Z -graded setting. Our main result classifies inner-faithful actions of generalized Taft algebras on quantum generalized Weyl algebras which respect the Z -grading. We also show that generically the invariant rings of Taft actions on quantum generalized Weyl algebras are commutative rings.
abstractGer	We study actions of pointed Hopf algebras in the Z -graded setting. Our main result classifies inner-faithful actions of generalized Taft algebras on quantum generalized Weyl algebras which respect the Z -grading. We also show that generically the invariant rings of Taft actions on quantum generalized Weyl algebras are commutative rings.
abstract_unstemmed	We study actions of pointed Hopf algebras in the Z -graded setting. Our main result classifies inner-faithful actions of generalized Taft algebras on quantum generalized Weyl algebras which respect the Z -grading. We also show that generically the invariant rings of Taft actions on quantum generalized Weyl algebras are commutative rings.
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title_short	Pointed Hopf actions on quantum generalized Weyl algebras
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doi_str	10.1016/j.jalgebra.2022.03.005
up_date	2024-07-06T17:01:58.293Z
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Pointed Hopf actions on quantum generalized Weyl algebras

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