Frontiers of Mathematics in China >
Irreducible function bases of isotropic invariants of a third order three-dimensional symmetric and traceless tensor
Received date: 20 Sep 2018
Accepted date: 14 Jan 2019
Published date: 22 Mar 2019
Copyright
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.
Yannan CHEN , Shenglong HU , Liqun QI , Wennan ZOU . Irreducible function bases of isotropic invariants of a third order three-dimensional symmetric and traceless tensor[J]. Frontiers of Mathematics in China, 2019 , 14(1) : 1 -16 . DOI: 10.1007/s11464-019-0748-x
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