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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

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...

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Published in: Journal of Algebra
ISSN: 00218693
Published: 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa27394
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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 College of 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
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publishDate 2016
institution Swansea University
issn 00218693
doi_str_mv 10.1016/j.jalgebra.2016.04.018
college_str College of Science
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hierarchy_top_title College of Science
hierarchy_parent_id collegeofscience
hierarchy_parent_title College of Science
department_str Mathematics{{{_:::_}}}College of Science{{{_:::_}}}Mathematics
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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 2016-08-15T03:38:42Z
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