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Rong-Chuan Xiong

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Preprint Aug 2026

Exact Factorizations of Rank-One Pointed Hopf Algebras in Positive Characteristic, I

We classify exact factorizations of the third-type rank-one pointed Hopf algebras over an algebraically closed field of positive characteristic. The main step is a complete classification of matched pairs between such an algebra and a group algebra. It turns out that the group-like part must form a matched pair of fini...

Rong-Chuan Xiong · 0 citations

Preprint Sep 2026

A $q$-Weyl Freeness Principle for Nichols Algebras and Pointed Hopf Algebras of Square-Free Dimension

Let $H$ be a pointed Hopf algebra of square-free dimension over an algebraically closed field of characteristic $p>0$. We prove that either $H$ is a group algebra or $\dim H/|\G(H)|=p$, and that in the latter case $H$ belongs to exactly one of two explicit families of rank-one pointed Hopf algebras. We develop a trunca...

Rong-Chuan Xiong · 0 citations

Preprint Sep 2026

Normalized quadratic extensions of pointed Hopf algebras

Let $L$ be a finite-dimensional pointed Hopf algebra over an algebraically closed field. We establish an intrinsic characterization of index-two extensions: every Hopf algebra $H$ containing $L$ as a Hopf subalgebra and satisfying $H_0=L_0$ and $\dim H=2\dim L$ is a normalized quadratic extension of $L$. For a fixed su...

Rong-Chuan Xiong · 0 citations