2025/11/21 by Ryuji Tanimoto, Tanimoto, Ryuji
Mathematics · #Finite Group Theory Research #Advanced Algebra and Geometry #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2511.17289
Let k be an algebraically closed field of positive characteristic p and let \mathbbGa denote the additive group of k. Let n ≥ 1 and let \rm Mat(n, k[T])E denote the set of all exponential matrices of \rm Mat(n, k[T]). Let 𝔼≥ 0(n, k) denote the set of all group homomorphisms from (ℤ/pℤ)r to \rm GL(n, k), where r ranges over all non-negative integers. In the first, we show that there exists a one-to-one correspondence between the set \rm Mat(n, k[T])E and the set of all \mathbbGa-actions on ℙn - 1. In the second, we show that there exists a one-to-one correspondence between 𝔼≥ 0(n, k) and the set \rm Mat(n, k[T])E × ℤ≥ 0.