Equivalence of Paths under the Action of the Real Representation of Sp(n)
Equivalence of Paths under the Action of the Real Representation of Sp(n)作者机构：Department of Mathematics National University of Uzbekistan named after Mirzo Ulugbek Tashkent Uzbekistan Department of Mathematics and Computer Science Fergana State University Fergana Uzbekistan
出 版 物：《Journal of Applied Mathematics and Physics》 (应用数学与应用物理（英文）)
年 卷 期：2022年第10卷第5期
页 面：1837-1858页
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Real Representation Differential Invariant Differential Generators Path in a Finite-Dimensional Space
摘 要：In this article, we will consider questions of G-equivalence of paths for the case when G was the group of the real representation of a symplectic transformation in an n-dimensional quaternion vector space. In determining the solution of this problem, we give an explicit description of differential generators of a differential field of differential rational functions that are invariant under the action of this group. Necessary and sufficient conditions for the G-equivalence of paths in a 4n-dimensional real space are obtained with the help of differential generators.
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