کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6414227 | 1630454 | 2016 | 25 صفحه PDF | دانلود رایگان |
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 pseudotwistor [Panaite and Van Oystaeyen (2015) [15]] 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 bialgebras hereby introduced as a natural extension of infinitesimal bialgebras [Aguiar (2000) [3]].
Journal: Journal of Algebra - Volume 460, 15 August 2016, Pages 1-25