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## Section: New Results

### Skew-Symmetric Tensor Decomposition

Participant : Bernard Mourrain.

In [2], we introduce the “skew apolarity lemma" and we use it to give algorithms for the skew-symmetric rank and the decomposition of tensors in ${\wedge }^{d}{V}_{ℂ}$ with $d\le 3$ and $dim{V}_{ℂ}\le 8$. New algorithms to compute the rank and a minimal decomposition of a tri-tensor are also presented.

This is a joint work with Enrique Arrondo (UCM - Universidad Complutense de Madrid, Spain), Alessandra Bernardi (Department of Mathematics, University of Trento, Italy) Pedro Macias Marques (Departamento de Matemática da Universidade de Évora, Spain).