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Irreducible function bases of isotropic invariants of a third order three-dimensional symmetric and traceless tensor |
Yannan CHEN1, Shenglong HU2, Liqun QI3( ), Wennan ZOU4 |
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 |
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Abstract 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.
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Minimal integrity basis
irreducible function basis
symmetric and traceless tensor
syzygy
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Corresponding Author(s):
Liqun QI
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Issue Date: 22 March 2019
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