| Title: |
Polynomial maps with constants on split octonion algebras |
| Authors: |
Panja, Saikat, Saini, Prachi, Singh, Anupam |
| Publication Year: |
2025 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Rings and Algebras, Mathematics - Group Theory, 16S50, 11P05 |
| More Details: |
Let $\mathbf{O}(\mathbb{F})$ be the split octonion algebra over an algebraically closed field $\mathbb{F}$. For positive integers $k_1, k_2\geq 2$, we study surjectivity of the map $A_1(x^{k_1}) + A_2(y^{k_2}) \in \mathbf{O}(\mathbb{F})\langle x, y\rangle$ on $\mathbf{O}(\mathbb{F})$. For this, we use the orbit representatives of the ${G}_2(\mathbb{F})$-action on $\mathbf{O}(\mathbb{F}) \times \mathbf{O}(\mathbb{F}) $ for the tuple $(A_1, A_2)$, and characterize the ones which give a surjective map. |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2503.06221 |
| Accession Number: |
edsarx.2503.06221 |
| Database: |
arXiv |
