Isotropic polynomial invariants of Hall tensor. (English) Zbl 1416.15020
Summary: The Hall tensor emerges from the study of the Hall effect, an important magnetic effect observed in electric conductors and semiconductors. The Hall tensor is third-order and three-dimensional, whose first two indices are skew-symmetric. This paper investigates the isotropic polynomial invariants of the Hall tensor by connecting it with a second-order tensor via the third-order Levi-Civita tensor. A minimal isotropic integrity basis with 10 invariants for the Hall tensor is proposed. Furthermore, it is proved that this minimal integrity basis is also an irreducible isotropic function basis of the Hall tensor.
MSC:
| 15A69 | Multilinear algebra, tensor calculus |
| 15A72 | Vector and tensor algebra, theory of invariants |
Keywords:
isotropic polynomial invariant; irreducibility; function basis; integrity basis; Hall tensorReferences:
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