Canonical forms of 2\× 3 \× 3 tensors over the real field,\n algebraically closed fields, and finite fields

2014/11/21 by Michel Lavrauw, Lavrauw, Michel, John Sheekey +1
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1411.5910

openalex publication_date 2014/11/21 · openalex created_date 2022/09/05 · openalex updated_date 2026/07/28

Abstract

We classify the orbits of elements of the tensor product spaces\n mathbbF²\⊗ mathbbF³ \⊗ mathbbF³ for all finite;\nreal; and algebraically closed fields under the action of two natural groups.\nThe result can also be interpreted as the classification of the orbits in the\n17-dimensional projective space of the Segre variety product of a projective\nline and two projective planes. This extends the classification of the orbits\nin the 7-dimensional projective space of the Segre variety product of three\nprojective lines [M. Lavrauw and J. Sheekey: Orbits of the stabiliser group of\nthe Segre variety product of three projective lines, Finite Fields Appl.\n(2014)]. The proof is geometric in nature, relies on properties of the Segre\nembedding, and uses the terminology of projective spaces.\n

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