2017/12/06 by Yannan Chen, Chen, Yannan, Shenglong Hu +5 · 1 citation
Computer Science · Mathematics · #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1712.02087
openalex publication_date 2017/12/06 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
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 polynomial syzygy relation among the four invariants of that basis, i.e., these four invariants are algebraically independent.