Decomposable critical tensors
It is observed that, in \(\wedge^m V\), the notions of critical element and decomposable element coincide. Known results for decomposable elements of \(\wedge^m V\) are extended to critical elements. The authors prove that a Grassmann tensor is critical if and only if it is Grassmann decomposable. This observation allow them to conclude that the first of the main theorems of this paper generalizes the well known result. They conduct a family of generalized Plücker polynomials for characterizing the set of critical decomposable tensors. Section 2 is a combinatorial tour. In Section 3, the relation between the principal result of this article and the classical results on Grassmann spaces is established. Section 4 is on pre-image families and the reach of a tensor. Section 5 is on decomposable tensors. The main purpose of Section 6 is to construct a family of polynomials characterizing the criticality of a decomposable tensor.
scientific article; zbMATH DE number 5016226