Irreducible function bases of isotropic invariants of a third order three-dimensional symmetric and traceless tensor  

作　　者：Yannan CHEN Shenglong HU Liqun QI Wennan ZOU 

机构地区：[1]School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China [2]Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou 310018, China [3]Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China [4]Institute for Advanced Study, Nanchang University, Nanchang 330031, China

出　　处：《Frontiers of Mathematics in China》2019年第1期1-16,共16页中国高等学校学术文摘·数学（英文）

基　　金：National Natural Science Foundation of China (Grant Nos. 1177132& 11771405, 1157117& 11372124);Hong Kong Research Grant Council (Grant Nos. PolyU 15302114, 15300715, 15301716, 15300717).

摘　　要：Third order three-dimensional symmetric and traceless tensors play an important role in physics and tensor representation theory. A minimal integrity basis of a third order three-dimensional symmetric and traceless tensor has four invariants with degrees two, four, six, and ten, respectively. In this paper, we show that any minimal integrity basis of a third order three-dimensional symmetric and traceless tensor is also an irreducible function basis of that tensor, and there is no syzygy relation among the four invariants of that basis, i.e., these four invariants are algebraically independent.

关 键 词：Minimal integrity BASIS IRREDUCIBLE FUNCTION BASIS SYMMETRIC and TRACELESS TENSOR syzygy 

分 类 号：O[理学]