Adjacency preserving maps on symmetric tensors

Let r and s be positive integers such that r 2. Let U and V be vector spaces over fields F and K, respectively, such that dim U 3 and F has at least r + 1 elements. In this paper, we characterize surjective maps psi : S r U -> S s V preserving adjacency in both directions on symmetric tensors of...

全面介紹

Saved in:
書目詳細資料
Main Authors: Chooi, Wai Leong, Lau, Jinting
格式: Article
出版: Elsevier 2024
主題:
在線閱讀:http://eprints.um.edu.my/45418/
https://doi.org/10.1016/j.laa.2024.02.029
標簽: 添加標簽
沒有標簽, 成為第一個標記此記錄!
機構: Universiti Malaya
實物特徵
總結:Let r and s be positive integers such that r 2. Let U and V be vector spaces over fields F and K, respectively, such that dim U 3 and F has at least r + 1 elements. In this paper, we characterize surjective maps psi : S r U -> S s V preserving adjacency in both directions on symmetric tensors of finite order, which generalizes Hua's fundamental theorem of geometry of symmetric matrices. We give examples showing the indispensability of the assumptions dim U 3 and the cardinality | F| r + 1 in our result. (c) 2024 Published by Elsevier Inc.