University of Mohaghegh Ardabili Journal of Finsler Geometry and its Applications 2783-0500 4 1 2023 07 01 The relation between automorphism group and isometry group of left invariant (α, β)-metrics 81 87 2316 10.22098/jfga.2023.12784.1088 EN Hamid Reza Salimi Moghaddam Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, 81746-73441-Iran. Masumeh Nejadahmad Department of Mathematics, Isfahan University of Technology, Iran. Journal Article 2023 04 25 Let F be an (α,β)-metric which is defined by a left invariant vector field and a left invariant Riemannian metric on a simply connected real Lie group G. We consider the automorphism and isometry groups of the Finsler manifold (G,F) and their intersection. We prove that for an arbitrary left invariant vector field X and any compact subgroup K of automorphisms which X is invariant under them, there exists an (α,β)-metric such that K is a subgroup of its isometry group. https://jfga.uma.ac.ir/article_2316_20d7531affdcc518e837bc20a1997289.pdf