Simultaneous invariants for systems of tensors of orders two and four. (Simultaninvarianten bei Systemen zwei- und vierstufiger Tensoren.) (German) Zbl 0859.15020
Summary: Following Hilbert’s Theorem, to each system of tensors there exists an integrity basis, i.e. a bounded number of invariants such that every arbitrary invariant can be represented as an entire rational function of the elements of this integrity basis. Besides of the invariants of the single tensors to an integrity basis of a system of tensors also belong simultaneous invariants, i.e. invariants being formed of the coordinates of several tensors. In the present paper, irreducible systems of simultaneous invariants are constructed and discussed for tensors of orders two and four in the two-, three-, and four-dimensional spaces.
MSC:
| 15A72 | Vector and tensor algebra, theory of invariants |
| 13A50 | Actions of groups on commutative rings; invariant theory |
| 74E10 | Anisotropy in solid mechanics |
| 74G70 | Stress concentrations, singularities in solid mechanics |
| 74H35 | Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics |
Keywords:
Hilbert’s theorem; system of tensors; integrity basis; simultaneous invariants; irreducible systemsReferences:
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