Classification of subspaces in \mathbbF²⊗ \mathbbF³ and orbits in \mathbbF²⊗ \mathbbF³⊗ \mathbbF^r

2015/03/13 by Michel Lavrauw, Lavrauw, Michel, John Sheekey +1
Mathematics · #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #math.AG #math.CO

paper · pdf · doi:10.48550/arxiv.1503.07894

arxiv created 2016/01/27 · arxiv updated 2016/01/28

Abstract

This paper contains the classification of the orbits of elements of the tensor product spaces \mathbbF²⊗ \mathbbF³ ⊗\mathbbF^r, r≥ 1, under the action of two natural groups, for all finite; real; and algebraically closed fields. For each of the orbits we determine: a canonical form; the tensor rank; the rank distribution of the contraction spaces; and a geometric description. The proof is based on the study of the contraction spaces in PG(\mathbbF²⊗\mathbbF³) and is geometric in nature. Although the main focus is on finite fields, the techniques are mostly field independent.

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