TY - JOUR
T1 - Irreducible function bases of isotropic invariants of a third order three-dimensional symmetric and traceless tensor
AU - Chen, Yannan
AU - Hu, Shenglong
AU - Qi, Liqun
AU - Zou, Wennan
PY - 2019/2/1
Y1 - 2019/2/1
N2 - 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.
AB - 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.
KW - irreducible function basis
KW - Minimal integrity basis
KW - symmetric and traceless tensor
KW - syzygy
UR - http://www.scopus.com/inward/record.url?scp=85062801429&partnerID=8YFLogxK
U2 - 10.1007/s11464-019-0748-x
DO - 10.1007/s11464-019-0748-x
M3 - Journal article
AN - SCOPUS:85062801429
SN - 1673-3452
VL - 14
JO - Frontiers of Mathematics in China
JF - Frontiers of Mathematics in China
IS - 1
ER -