发表机构
University of Regina（雷吉纳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文刻画了实数矩阵空间上保持强无限可分矩阵和无限可分非负矩阵的双射线性映射，分别采用Zariski稠密技术和锥保持方法。
AI 中文摘要
无限可分非负矩阵是一个逐项非负矩阵，它允许对每个正整数 $m$，在通常矩阵乘法下存在逐项非负的 $m$ 次根；当它此外还可逆时，称为强无限可分矩阵。对此类矩阵的研究起源于无限可分概率分布理论和马尔可夫矩阵的嵌入问题，并与连续单参数半群密切相关；在可逆情形下，这种联系可以通过指数映射自然地描述。本文刻画了 $M_n(\mathbb{R})$ 上保持强无限可分矩阵和无限可分非负矩阵的双射线性映射。在前一情形中，我们将反函数定理与 Zariski 稠密技术相结合，利用 Fallat 和 Mondal 最近在线性保持算子理论中发展的 Zariski 稠密方法 [\textit{Proc. Amer. Math. Soc.}, 2026]。在后一情形中，我们首先证明保持无限可分性迫使保持逐项非负矩阵锥，然后利用无限可分性所提供的额外结构来完成刻画。
英文摘要
An infinitely divisible nonnegative matrix is an entry-wise nonnegative matrix that admits an entry-wise nonnegative $m$th root, with respect to usual matrix multiplication, for every positive integer $m$; it is called strongly infinitely divisible when it is, in addition, invertible. The study of such matrices has its origins in the theory of infinitely divisible probability distributions and the embedding problem for Markov matrices and is closely connected with continuous one-parameter semigroups; in the invertible case, this connection admits a natural description in terms of the exponential map. In this paper, we characterize the bijective linear maps on $M_n(\mathbb{R})$ that preserve strongly infinitely divisible matrices and infinitely divisible nonnegative matrices. In the former case, we combine the Inverse Function Theorem with Zariski-density techniques, using the Zariski-density approach recently developed in linear preserver theory by Fallat and Mondal [\textit{Proc. Amer. Math. Soc.}, 2026]. In the latter case, we first show that preserving infinite divisibility forces preservation of the cone of entry-wise nonnegative matrices and then exploit the additional structure afforded by infinite divisibility to complete the characterization.
Comments20 pages
