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arXiv · 2602.17328

Frobenius extensions about centralizer matrix algebras

Qikai Wang·Haiyan Zhu
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Abstract

This paper investigates the conditions under which the centralizer algebra $S_n(c,R)$ of a matrix $ c\in M_n(R)$ is a (separable) Frobenius extension of the base algebra $R$. For an algebra $R$ over an integral domain $\mathbb{k}$, we provide necessary and sufficient conditions for $S_n(c,R)/R$ to be a (separable) Frobenius extension when $c$ is in Jordan canonical form with eigenvalues in $\mathbb{k}$. We extend this analysis to arbitrary matrices over a field and derive conditions for matrix diagonalizability through Frobenius extensions.

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Qikai Wang, Haiyan Zhu. 2026-02-19. Frobenius extensions about centralizer matrix algebras. https://doi.org/10.1016/j.laa.2025.07.002

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