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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Acknowledgements
This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11771328, 11771405, 11571178, 11372124) and the Hong Kong Research Grant Council (Grant Nos. PolyU 15302114, 15300715, 15301716, 15300717).
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Chen, Y., Hu, S., Qi, L. et al. Irreducible function bases of isotropic invariants of a third order three-dimensional symmetric and traceless tensor. Front. Math. China 14, 1–16 (2019). https://doi.org/10.1007/s11464-019-0748-x
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DOI: https://doi.org/10.1007/s11464-019-0748-x