Adjacency preserving functions on symmetric elements and linear preservers of non-zero decomposable symmetric tensors |
| |
Authors: | Ming-Huat Lim |
| |
Institution: | 1. Institute of Mathematical Sciences, University of Malaya , 50603 Kuala Lumpur , Malaysia limmh@um.edu.my |
| |
Abstract: | Let A be a non-empty set and m be a positive integer. Let ≡ be the equivalence relation defined on A m such that (x 1, …, x m ) ≡ (y 1, …, y m ) if there exists a permutation σ on {1, …, m} such that y σ(i) = x i for all i. Let A (m) denote the set of all equivalence classes determined by ≡. Two elements X and Y in A (m) are said to be adjacent if (x 1, …, x m?1, a) ∈ X and (x 1, …, x m?1, b) ∈ Y for some x 1, …, x m?1 ∈ A and some distinct elements a, b ∈ A. We study the structure of functions from A (m) to B (n) that send adjacent elements to adjacent elements when A has at least n + 2 elements and its application to linear preservers of non-zero decomposable symmetric tensors. |
| |
Keywords: | adjacency preserving function symmetric power decomposable symmetric tensor |
|
|