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ON THE HOCHSCHILD HOMOLOGY OF INVOLUTIVE ALGEBRAS

RAMSÈS FERNÀNDEZ-VALÈNCIA, Jeffrey Giansiracusa Orcid Logo

Glasgow Mathematical Journal, Volume: 60, Issue: 01, Pages: 187 - 198

Swansea University Author: Jeffrey Giansiracusa Orcid Logo

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DOI (Published version): 10.1017/S0017089516000653

Abstract

We study the homological algebra of bimodules over involutive associative algebras. We show that Braun’s definition of involutive Hochschild cohomology in terms of the complex of involution-preserving derivations is indeed computing a derived functor: the Z/2-invariants intersected with the center....

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Published in: Glasgow Mathematical Journal
ISSN: 0017-0895 1469-509X
Published: Cambridge University Press 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa30925
first_indexed 2016-11-04T05:30:19Z
last_indexed 2021-02-24T03:47:52Z
id cronfa30925
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spelling 2021-02-23T14:10:23.0393591 v2 30925 2016-11-03 ON THE HOCHSCHILD HOMOLOGY OF INVOLUTIVE ALGEBRAS 03c4f93e1b94af60eb0c18c892b0c1d9 0000-0003-4252-0058 Jeffrey Giansiracusa Jeffrey Giansiracusa true false 2016-11-03 MACS We study the homological algebra of bimodules over involutive associative algebras. We show that Braun’s definition of involutive Hochschild cohomology in terms of the complex of involution-preserving derivations is indeed computing a derived functor: the Z/2-invariants intersected with the center. We then introduce the corresponding involutive Hochschild homology theory and describe it as the derived functor of the pushout of Z/2-coinvariants and abelianization. Journal Article Glasgow Mathematical Journal 60 01 187 198 Cambridge University Press 0017-0895 1469-509X Hochschild homology, involution, involutive algebras, bimodules 31 12 2018 2018-12-31 10.1017/S0017089516000653 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2021-02-23T14:10:23.0393591 2016-11-03T21:30:45.3401905 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics RAMSÈS FERNÀNDEZ-VALÈNCIA 1 Jeffrey Giansiracusa 0000-0003-4252-0058 2 0030925-03112016213150.pdf GMJ-15.0128.R1.pdf 2016-11-03T21:31:50.4570000 Output 181271 application/pdf Accepted Manuscript true 2017-08-07T00:00:00.0000000 true
title ON THE HOCHSCHILD HOMOLOGY OF INVOLUTIVE ALGEBRAS
spellingShingle ON THE HOCHSCHILD HOMOLOGY OF INVOLUTIVE ALGEBRAS
Jeffrey Giansiracusa
title_short ON THE HOCHSCHILD HOMOLOGY OF INVOLUTIVE ALGEBRAS
title_full ON THE HOCHSCHILD HOMOLOGY OF INVOLUTIVE ALGEBRAS
title_fullStr ON THE HOCHSCHILD HOMOLOGY OF INVOLUTIVE ALGEBRAS
title_full_unstemmed ON THE HOCHSCHILD HOMOLOGY OF INVOLUTIVE ALGEBRAS
title_sort ON THE HOCHSCHILD HOMOLOGY OF INVOLUTIVE ALGEBRAS
author_id_str_mv 03c4f93e1b94af60eb0c18c892b0c1d9
author_id_fullname_str_mv 03c4f93e1b94af60eb0c18c892b0c1d9_***_Jeffrey Giansiracusa
author Jeffrey Giansiracusa
author2 RAMSÈS FERNÀNDEZ-VALÈNCIA
Jeffrey Giansiracusa
format Journal article
container_title Glasgow Mathematical Journal
container_volume 60
container_issue 01
container_start_page 187
publishDate 2018
institution Swansea University
issn 0017-0895
1469-509X
doi_str_mv 10.1017/S0017089516000653
publisher Cambridge University 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
document_store_str 1
active_str 0
description We study the homological algebra of bimodules over involutive associative algebras. We show that Braun’s definition of involutive Hochschild cohomology in terms of the complex of involution-preserving derivations is indeed computing a derived functor: the Z/2-invariants intersected with the center. We then introduce the corresponding involutive Hochschild homology theory and describe it as the derived functor of the pushout of Z/2-coinvariants and abelianization.
published_date 2018-12-31T19:01:39Z
_version_ 1821342642159484928
score 11.04748

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