A remark on the Hochschild dimension of liberated quantum groups

Brzezinski, Tomasz; Krähmer, Ulrich; Buachalla, Réamonn Ó; Strung, Karen R.

doi:10.4171/jncg/572

Journal article 268 views 57 downloads

A remark on the Hochschild dimension of liberated quantum groups

Tomasz Brzezinski

, Ulrich Krähmer

, Réamonn Ó Buachalla

, Karen R. Strung

Journal of Noncommutative Geometry, Volume: 19, Issue: 2, Pages: 647 - 656

Swansea University Author: Tomasz Brzezinski

PDF | Version of Record

This work is licensed under a CC BY 4.0 license.
Download (271.16KB)

Check full text

DOI (Published version): 10.4171/jncg/572

Abstract

Let A be a Hopf algebra equipped with a projection onto the coordinate Hopf algebra O(G) of a semisimple algebraic group G. It is shown that if A admits a suitably non-degenerate comodule V and the induced G-module structure of V is non-trivial, then the third Hochschild homology group of A is non-t...

Full description

Published in:	Journal of Noncommutative Geometry
ISSN:	1661-6952 1661-6960
Published:	EMS Press 2025
Online Access:	Check full text
URI:	https://cronfa.swan.ac.uk/Record/cronfa69804

first_indexed	2025-06-24T09:58:21Z
last_indexed	2025-07-22T05:04:07Z
id	cronfa69804
recordtype	SURis
fullrecord	<?xml version="1.0"?><rfc1807><datestamp>2025-07-21T14:09:11.6929268</datestamp><bib-version>v2</bib-version><id>69804</id><entry>2025-06-24</entry><title>A remark on the Hochschild dimension of liberated quantum groups</title><swanseaauthors><author><sid>30466d840b59627325596fbbb2c82754</sid><ORCID>0000-0001-6270-3439</ORCID><firstname>Tomasz</firstname><surname>Brzezinski</surname><name>Tomasz Brzezinski</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2025-06-24</date><deptcode>MACS</deptcode><abstract>Let A be a Hopf algebra equipped with a projection onto the coordinate Hopf algebra O(G) of a semisimple algebraic group G. It is shown that if A admits a suitably non-degenerate comodule V and the induced G-module structure of V is non-trivial, then the third Hochschild homology group of A is non-trivial.</abstract><type>Journal Article</type><journal>Journal of Noncommutative Geometry</journal><volume>19</volume><journalNumber>2</journalNumber><paginationStart>647</paginationStart><paginationEnd>656</paginationEnd><publisher>EMS Press</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>1661-6952</issnPrint><issnElectronic>1661-6960</issnElectronic><keywords>Hopf algebras, Hochschild cohomology, quantum groups, noncommutative geometry</keywords><publishedDay>3</publishedDay><publishedMonth>4</publishedMonth><publishedYear>2025</publishedYear><publishedDate>2025-04-03</publishedDate><doi>10.4171/jncg/572</doi><url>https://ems.press/journals/jncg/articles/14297824</url><notes/><college>COLLEGE NANME</college><department>Mathematics and Computer Science School</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>MACS</DepartmentCode><institution>Swansea University</institution><apcterm>Not Required</apcterm><funders>International Centre for Mathematical Sciences; National Science Centre, Poland, grant no. 2019/35/B/ST1/01115; DFG grant “Cocommutative comonoids” (KR 5036/2-1); Charles University PRIMUS grant “Spectral Noncommutative Geometry of Quantum Flag Manifolds” PRIMUS/21/SCI/026; CaLIGOLA MSCA2021-SE- 01-101086123; GAČR project 20-17488Y; Institute of Mathematics, Czech Academy of Sciences, RVO: 6798584.</funders><projectreference/><lastEdited>2025-07-21T14:09:11.6929268</lastEdited><Created>2025-06-24T10:41:09.5172285</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Mathematics and Computer Science - Mathematics</level></path><authors><author><firstname>Tomasz</firstname><surname>Brzezinski</surname><orcid>0000-0001-6270-3439</orcid><order>1</order></author><author><firstname>Ulrich</firstname><surname>Krähmer</surname><orcid>0000-0002-5350-6932</orcid><order>2</order></author><author><firstname>Réamonn Ó</firstname><surname>Buachalla</surname><orcid>0000-0002-5940-7513</orcid><order>3</order></author><author><firstname>Karen R.</firstname><surname>Strung</surname><orcid>0000-0002-8445-4637</orcid><order>4</order></author></authors><documents><document><filename>69804__34555__d5161fc8614646ab9dc1304308f7de89.pdf</filename><originalFilename>69804.VOR.pdf</originalFilename><uploaded>2025-06-24T10:55:26.7337993</uploaded><type>Output</type><contentLength>277671</contentLength><contentType>application/pdf</contentType><version>Version of Record</version><cronfaStatus>true</cronfaStatus><documentNotes>This work is licensed under a CC BY 4.0 license.</documentNotes><copyrightCorrect>true</copyrightCorrect><language>eng</language><licence>https://creativecommons.org/licenses/by/4.0/</licence></document></documents><OutputDurs/></rfc1807>
spelling	2025-07-21T14:09:11.6929268 v2 69804 2025-06-24 A remark on the Hochschild dimension of liberated quantum groups 30466d840b59627325596fbbb2c82754 0000-0001-6270-3439 Tomasz Brzezinski Tomasz Brzezinski true false 2025-06-24 MACS Let A be a Hopf algebra equipped with a projection onto the coordinate Hopf algebra O(G) of a semisimple algebraic group G. It is shown that if A admits a suitably non-degenerate comodule V and the induced G-module structure of V is non-trivial, then the third Hochschild homology group of A is non-trivial. Journal Article Journal of Noncommutative Geometry 19 2 647 656 EMS Press 1661-6952 1661-6960 Hopf algebras, Hochschild cohomology, quantum groups, noncommutative geometry 3 4 2025 2025-04-03 10.4171/jncg/572 https://ems.press/journals/jncg/articles/14297824 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University Not Required International Centre for Mathematical Sciences; National Science Centre, Poland, grant no. 2019/35/B/ST1/01115; DFG grant “Cocommutative comonoids” (KR 5036/2-1); Charles University PRIMUS grant “Spectral Noncommutative Geometry of Quantum Flag Manifolds” PRIMUS/21/SCI/026; CaLIGOLA MSCA2021-SE- 01-101086123; GAČR project 20-17488Y; Institute of Mathematics, Czech Academy of Sciences, RVO: 6798584. 2025-07-21T14:09:11.6929268 2025-06-24T10:41:09.5172285 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Tomasz Brzezinski 0000-0001-6270-3439 1 Ulrich Krähmer 0000-0002-5350-6932 2 Réamonn Ó Buachalla 0000-0002-5940-7513 3 Karen R. Strung 0000-0002-8445-4637 4 69804__34555__d5161fc8614646ab9dc1304308f7de89.pdf 69804.VOR.pdf 2025-06-24T10:55:26.7337993 Output 277671 application/pdf Version of Record true This work is licensed under a CC BY 4.0 license. true eng https://creativecommons.org/licenses/by/4.0/
title	A remark on the Hochschild dimension of liberated quantum groups
spellingShingle	A remark on the Hochschild dimension of liberated quantum groups Tomasz Brzezinski
title_short	A remark on the Hochschild dimension of liberated quantum groups
title_full	A remark on the Hochschild dimension of liberated quantum groups
title_fullStr	A remark on the Hochschild dimension of liberated quantum groups
title_full_unstemmed	A remark on the Hochschild dimension of liberated quantum groups
title_sort	A remark on the Hochschild dimension of liberated quantum groups
author_id_str_mv	30466d840b59627325596fbbb2c82754
author_id_fullname_str_mv	30466d840b59627325596fbbb2c82754_***_Tomasz Brzezinski
author	Tomasz Brzezinski
author2	Tomasz Brzezinski Ulrich Krähmer Réamonn Ó Buachalla Karen R. Strung
format	Journal article
container_title	Journal of Noncommutative Geometry
container_volume	19
container_issue	2
container_start_page	647
publishDate	2025
institution	Swansea University
issn	1661-6952 1661-6960
doi_str_mv	10.4171/jncg/572
publisher	EMS Press
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
url	https://ems.press/journals/jncg/articles/14297824
document_store_str	1
active_str	0
description	Let A be a Hopf algebra equipped with a projection onto the coordinate Hopf algebra O(G) of a semisimple algebraic group G. It is shown that if A admits a suitably non-degenerate comodule V and the induced G-module structure of V is non-trivial, then the third Hochschild homology group of A is non-trivial.
published_date	2025-04-03T05:29:08Z
_version_	1851097925618237440
score	11.089572

A remark on the Hochschild dimension of liberated quantum groups

Similar Items