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Actions of Hopf quasigroups

Tomasz Brzezinski Orcid Logo

Communications in Algebra, Volume: 40, Issue: 2, Pages: 681 - 696

Swansea University Author: Tomasz Brzezinski Orcid Logo

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DOI (Published version): 10.1080/00927872.2010.535588

Abstract

Definitions of actions of Hopf quasigroups are discussed in the context of Long dimodules and smash products. In particular, Long dimodules are defined for Hopf quasigroups and coquasigroups, and solutions to Militaru's -equation are constructed. A necessary compatibility condition between acti...

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Published in: Communications in Algebra
Published: 2012
URI: https://cronfa.swan.ac.uk/Record/cronfa8009
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spelling 2015-03-25T09:56:46.3905372 v2 8009 2012-02-22 Actions of Hopf quasigroups 30466d840b59627325596fbbb2c82754 0000-0001-6270-3439 Tomasz Brzezinski Tomasz Brzezinski true false 2012-02-22 SMA Definitions of actions of Hopf quasigroups are discussed in the context of Long dimodules and smash products. In particular, Long dimodules are defined for Hopf quasigroups and coquasigroups, and solutions to Militaru's -equation are constructed. A necessary compatibility condition between action and multiplication of a Hopf quasigroup acting on its quasimodule Hopf quasigroup for a smash product construction is derived. This necessary condition takes the form of the associativity of the action up to an antipodal operation. In the case of a Hopf quasigroup with a bijective antipode it is simply the associativity of the action, a condition assumed a priori by Klim and Majid in their original construction of smash products of Hopf quasigroups. Journal Article Communications in Algebra 40 2 681 696 31 12 2012 2012-12-31 10.1080/00927872.2010.535588 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2015-03-25T09:56:46.3905372 2012-02-22T13:37:04.0000000 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Tomasz Brzezinski 0000-0001-6270-3439 1
title Actions of Hopf quasigroups
spellingShingle Actions of Hopf quasigroups
Tomasz Brzezinski
title_short Actions of Hopf quasigroups
title_full Actions of Hopf quasigroups
title_fullStr Actions of Hopf quasigroups
title_full_unstemmed Actions of Hopf quasigroups
title_sort Actions of Hopf quasigroups
author_id_str_mv 30466d840b59627325596fbbb2c82754
author_id_fullname_str_mv 30466d840b59627325596fbbb2c82754_***_Tomasz Brzezinski
author Tomasz Brzezinski
author2 Tomasz Brzezinski
format Journal article
container_title Communications in Algebra
container_volume 40
container_issue 2
container_start_page 681
publishDate 2012
institution Swansea University
doi_str_mv 10.1080/00927872.2010.535588
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 0
active_str 0
description Definitions of actions of Hopf quasigroups are discussed in the context of Long dimodules and smash products. In particular, Long dimodules are defined for Hopf quasigroups and coquasigroups, and solutions to Militaru's -equation are constructed. A necessary compatibility condition between action and multiplication of a Hopf quasigroup acting on its quasimodule Hopf quasigroup for a smash product construction is derived. This necessary condition takes the form of the associativity of the action up to an antipodal operation. In the case of a Hopf quasigroup with a bijective antipode it is simply the associativity of the action, a condition assumed a priori by Klim and Majid in their original construction of smash products of Hopf quasigroups.
published_date 2012-12-31T03:10:02Z
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score 11.014067

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