Polynomial maps with constants on split octonion algebras

2025/03/08 by Panja, Saikat, Saini, Prachi, Singh, Anupam · 1 citation
#11P05 #16S50 #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2503.06221

Abstract

Let O(\mathbbF) be the split octonion algebra over an algebraically closed field \mathbbF. For positive integers k₁, k₂≥ 2, we study surjectivity of the map A₁(x^k₁) + A₂(y^k₂) ∈ O(\mathbbF)⟨ x, y⟩ on O(\mathbbF). For this, we use the orbit representatives of the G₂(\mathbbF)-action on O(\mathbbF) × O(\mathbbF) for the tuple (A₁, A₂), and characterize the ones which give a surjective map.

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