Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 21 (2025), 024, 36 pages      arXiv:2402.16704      https://doi.org/10.3842/SIGMA.2025.024

Twisted Post-Hopf Algebras, Twisted Relative Rota-Baxter Operators and Hopf Trusses

José Manuel Fernández Vilaboa ab, Ramón González Rodríguez ac and Brais Ramos Pérez ab
a) CITMAga, 15782 Santiago de Compostela, Spain
b) Departamento de Matemáticas, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15771 Santiago de Compostela, Spain
c) Departamento de Matemática Aplicada II, Universidade de Vigo, E.E. Telecomunicación, 36310 Vigo, Spain

Received November 19, 2024, in final form April 06, 2025; Published online April 15, 2025

Abstract
The present article is devoted to studying the categorical relationships between the categories of Hopf trusses, weak twisted post-Hopf algebras, introduced by Wang (2023), and weak twisted relative Rota-Baxter operators. The latter objects are a generalisation of the relative Rota-Baxter operators defined by Li-Sheng-Tang (2024), where the Rota-Baxter condition is modified through a cocycle. Under certain conditions, this work shows that the three aforementioned categories are equivalent.

Key words: braided monoidal category; Hopf algebra; Hopf truss; weak twisted post-Hopf algebra; weak twisted relative Rota-Baxter operator.

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