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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

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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...

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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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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 & 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].
College: Faculty of Science and Engineering
Start Page: 1
End Page: 25

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