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arXiv · 2503.04125

$\imath$Hopf algebras associated with self-dual Hopf algebras

Jiayi Chen·Shiquan Ruan
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Abstract

Motivated by the construction of $\imath$Hall algebras and $\Delta$-Hall algebras, we introduce $\imath$Hopf algebras associated with symmetrically self-dual Hopf algebras. We prove that the $\imath$Hopf algebra is an associative algebra with a unit, where the associativity relies on an analogue of Green's formula in the framework of Hopf algebras. As an application, we construct the $\imath$Taft algebra of dimension 4, which is proved to be isomorphic to the group algebra of $\mathbb{Z}/4\mathbb{Z}$.

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Jiayi Chen, Shiquan Ruan. 2025-03-06. $\imath$Hopf algebras associated with self-dual Hopf algebras. https://arxiv.org/abs/2503.04125

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