No Cover Image

Journal article 1182 views 176 downloads

Rota–Baxter systems, dendriform algebras and covariant bialgebras

Tomasz Brzeziński, Tomasz Brzezinski Orcid Logo

Journal of Algebra, Volume: 460, Pages: 1 - 25

Swansea University Author: Tomasz Brzezinski Orcid Logo

Check full text

DOI (Published version): 10.1016/j.jalgebra.2016.04.018

Abstract

A generalisation of the notion of a Rota-Baxter operator is proposed. This generalisation consists of two operators acting on an associative algebra and satisfying equations similar to the Rota-Baxter equation. Rota-Baxter operators of any weights and twisted Rota-Baxter operators are solutions of t...

Full description

Published in: Journal of Algebra
ISSN: 00218693
Published: 2016
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa27394
Tags: Add Tag
No Tags, Be the first to tag this record!
first_indexed 2016-04-23T01:11:41Z
last_indexed 2018-11-22T19:43:03Z
id cronfa27394
recordtype SURis
fullrecord <?xml version="1.0"?><rfc1807><datestamp>2018-11-22T15:56:00.9688430</datestamp><bib-version>v2</bib-version><id>27394</id><entry>2016-04-22</entry><title>Rota&#x2013;Baxter systems, dendriform algebras and covariant bialgebras</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>2016-04-22</date><deptcode>SMA</deptcode><abstract>A generalisation of the notion of a Rota-Baxter operator is proposed. This generalisation consists of two operators acting on an associative algebra and satisfying equations similar to the Rota-Baxter equation. Rota-Baxter operators of any weights and twisted Rota-Baxter operators are solutions of the proposed system. It is shown that dendriform algebra structures of a particular kind are equivalent to Rota-Baxter systems. It is shown further that a Rota-Baxter system induces a weak peudotwistor [F. Panaite &amp; F. Van Oystaeyen, Twisted algebras, twisted bialgebras and Rota-Baxter operators, arXiv:1502.05327 (2015)] which can be held responsible for the existence of a new associative product on the underlying algebra. Examples of solutions of Rota-Baxter systems are obtained from quasitriangular covariant bialge- bras hereby introduced as a natural extension of infinitesimal bialgebras [M. Aguiar, Infinitesimal Hopf algebras, [in:] New trends in Hopf algebra theory (La Falda, 1999), Contemp. Math., 267, Amer. Math. Soc., Providence, RI, (2000), pp. 1&#x2013;29].</abstract><type>Journal Article</type><journal>Journal of Algebra</journal><volume>460</volume><paginationStart>1</paginationStart><paginationEnd>25</paginationEnd><publisher/><issnPrint>00218693</issnPrint><keywords/><publishedDay>15</publishedDay><publishedMonth>8</publishedMonth><publishedYear>2016</publishedYear><publishedDate>2016-08-15</publishedDate><doi>10.1016/j.jalgebra.2016.04.018</doi><url/><notes/><college>COLLEGE NANME</college><department>Mathematics</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>SMA</DepartmentCode><institution>Swansea University</institution><apcterm/><lastEdited>2018-11-22T15:56:00.9688430</lastEdited><Created>2016-04-22T13:33:52.2744918</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>Brzezi&#x144;ski</surname><order>1</order></author><author><firstname>Tomasz</firstname><surname>Brzezinski</surname><orcid>0000-0001-6270-3439</orcid><order>2</order></author></authors><documents><document><filename>0027394-22042016133456.pdf</filename><originalFilename>rota_baxter.pdf</originalFilename><uploaded>2016-04-22T13:34:56.5670000</uploaded><type>Output</type><contentLength>308955</contentLength><contentType>application/pdf</contentType><version>Accepted Manuscript</version><cronfaStatus>true</cronfaStatus><embargoDate>2017-04-05T00:00:00.0000000</embargoDate><copyrightCorrect>true</copyrightCorrect></document></documents><OutputDurs/></rfc1807>
spelling 2018-11-22T15:56:00.9688430 v2 27394 2016-04-22 Rota–Baxter systems, dendriform algebras and covariant bialgebras 30466d840b59627325596fbbb2c82754 0000-0001-6270-3439 Tomasz Brzezinski Tomasz Brzezinski true false 2016-04-22 SMA A generalisation of the notion of a Rota-Baxter operator is proposed. This generalisation consists of two operators acting on an associative algebra and satisfying equations similar to the Rota-Baxter equation. Rota-Baxter operators of any weights and twisted Rota-Baxter operators are solutions of the proposed system. It is shown that dendriform algebra structures of a particular kind are equivalent to Rota-Baxter systems. It is shown further that a Rota-Baxter system induces a weak peudotwistor [F. Panaite & F. Van Oystaeyen, Twisted algebras, twisted bialgebras and Rota-Baxter operators, arXiv:1502.05327 (2015)] which can be held responsible for the existence of a new associative product on the underlying algebra. Examples of solutions of Rota-Baxter systems are obtained from quasitriangular covariant bialge- bras hereby introduced as a natural extension of infinitesimal bialgebras [M. Aguiar, Infinitesimal Hopf algebras, [in:] New trends in Hopf algebra theory (La Falda, 1999), Contemp. Math., 267, Amer. Math. Soc., Providence, RI, (2000), pp. 1–29]. Journal Article Journal of Algebra 460 1 25 00218693 15 8 2016 2016-08-15 10.1016/j.jalgebra.2016.04.018 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2018-11-22T15:56:00.9688430 2016-04-22T13:33:52.2744918 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Tomasz Brzeziński 1 Tomasz Brzezinski 0000-0001-6270-3439 2 0027394-22042016133456.pdf rota_baxter.pdf 2016-04-22T13:34:56.5670000 Output 308955 application/pdf Accepted Manuscript true 2017-04-05T00:00:00.0000000 true
title Rota–Baxter systems, dendriform algebras and covariant bialgebras
spellingShingle Rota–Baxter systems, dendriform algebras and covariant bialgebras
Tomasz Brzezinski
title_short Rota–Baxter systems, dendriform algebras and covariant bialgebras
title_full Rota–Baxter systems, dendriform algebras and covariant bialgebras
title_fullStr Rota–Baxter systems, dendriform algebras and covariant bialgebras
title_full_unstemmed Rota–Baxter systems, dendriform algebras and covariant bialgebras
title_sort Rota–Baxter systems, dendriform algebras and covariant bialgebras
author_id_str_mv 30466d840b59627325596fbbb2c82754
author_id_fullname_str_mv 30466d840b59627325596fbbb2c82754_***_Tomasz Brzezinski
author Tomasz Brzezinski
author2 Tomasz Brzeziński
Tomasz Brzezinski
format Journal article
container_title Journal of Algebra
container_volume 460
container_start_page 1
publishDate 2016
institution Swansea University
issn 00218693
doi_str_mv 10.1016/j.jalgebra.2016.04.018
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 generalisation of the notion of a Rota-Baxter operator is proposed. This generalisation consists of two operators acting on an associative algebra and satisfying equations similar to the Rota-Baxter equation. Rota-Baxter operators of any weights and twisted Rota-Baxter operators are solutions of the proposed system. It is shown that dendriform algebra structures of a particular kind are equivalent to Rota-Baxter systems. It is shown further that a Rota-Baxter system induces a weak peudotwistor [F. Panaite & F. Van Oystaeyen, Twisted algebras, twisted bialgebras and Rota-Baxter operators, arXiv:1502.05327 (2015)] which can be held responsible for the existence of a new associative product on the underlying algebra. Examples of solutions of Rota-Baxter systems are obtained from quasitriangular covariant bialge- bras hereby introduced as a natural extension of infinitesimal bialgebras [M. Aguiar, Infinitesimal Hopf algebras, [in:] New trends in Hopf algebra theory (La Falda, 1999), Contemp. Math., 267, Amer. Math. Soc., Providence, RI, (2000), pp. 1–29].
published_date 2016-08-15T03:33:12Z
_version_ 1763751381449048064
score 11.012678

Similar Items