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arXiv · 2501.15401

Splitting Property of quasitriangular Hopf algebras

Jinsong Wu·Kun Zhou
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Abstract

We investigate the splitting property of quasitriangular Hopf algebras through the lens of twisted tensor products. Specifically, we demonstrate that an infinite-dimensional quasitriangular Hopf algebra possesses the splitting property if it admits a factorizable quotient Hopf algebra. We also establish that the splitting property holds if there exists a full rank quotient Hopf algebra where the left and right coinvariants coincide. As a consequence, we obtain a new obstruction for quasitriangular structure in finite-dimensional Hopf algebras.

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Jinsong Wu, Kun Zhou. 2025-01-26. Splitting Property of quasitriangular Hopf algebras. https://arxiv.org/abs/2501.15401

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