Invariants of G₂ and Spin(7) in positive characteristic

2015/12/20 by Alexandr N. Zubkov, I. P. Shestakov, Zubkov, A. N. +1 · 2 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1512.06354

openalex publication_date 2015/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Invariants of G₂ and Spin(7), both acting on several copies of octonions, have been decribed in \citeschw2 over a ground field of characteristic zero. In the current manuscript, we extend this result to an arbitrary infinite field of odd characteristic. More precisely, we prove that the corresponding algebras of invariants are generated by the same invariants of degree at most 4 as in the case of a field of characteristic zero.

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