A new approach to Rota-Baxter coalgebras. (English) Zbl 1495.16028
In this paper the authors introduce the notion of Rota-Baxter linear equation system and construct examples working with idempotent coalgebra homomorphisms, projections of bialgebras, coalgebras in a category of Yetter-Drinfeld modules, quasigroups and finite left \(B\)-comodules associated a quasitriangular Hopf algebra \(B\). Also, in this article we can find a new technique to construct Rota-Baxter coalgebras of weight \(-1\) using Hopf quasicomodule quasicoalgebras. Finally, in Section 4 the authors present how to construct of Rota-Baxter coalgebras of weight \(-1\) by means of Hopf \(\pi\)-algebras.
Reviewer: Ramón González Rodríguez (Vigo)
MSC:
| 16T05 | Hopf algebras and their applications |
| 16W99 | Associative rings and algebras with additional structure |
Keywords:
Rota-Baxter coalgebras; Hopf quasicomodule coalgebras; Rota-Baxter linear equation systems; Yetter-Drinfel’d quasicomodule coalgebras; Hopf \(\pi\)-algebrasReferences:
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| [30] | Guodong Shi, Shuanhong Wang (corresponding author) School of Mathematics Southeast University |
| [31] | Nanjing, China E-mail: 230169403@seu.edu.cn shuanhwang@seu.edu.cn |
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