On polynomial automorphisms of spheres期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

On polynomial automorphisms of spheres

Authors:

Institution:

1. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, 87-100, Toruń, Chopina 12/18, Poland
2. Departamento de ‘Algebra, Geometría y Topología, Facultad de Ciencias, Universidad de Málaga, Campus Universitario de Teatinos, 29071, Málaga, Espa?a

Abstract:

Let K be an infinite field with characteristic different from two and $\mathbb{S}^n$ (K) the n-sphere over K. We show that ambient polynomial automorphisms of $\mathbb{S}^n$ (K) preserve the quadratic form x ₀² + ⋯ + x _n² and the group Aut ((K ⁿ⁺¹, $\mathbb{S}^n$ (K)) of such automorphisms of $\mathbb{S}^n$ (K) is isomorphic to the (n + 1)-orthogonal group O(n + 1, K) provided K is real. Next, the restriction map Aut (K ³, $\mathbb{S}^2$ (K)) → Aut ( $\mathbb{S}^2$ (K)) yields a surjection provided K is an algebraically closed field as well. Furthermore, for any such a field K, there is an imbedding

$KX_1 \ldots ,X_m ]^{\tfrac{{m(m - 1)}} {2} + mn} \to Aut (K^{2m + n} ,\mathbb{S}^{2m + n - 1} (K))$

. The second author was partially supported by the Ministerio de Ciencia y Tecnologia grant MTM2007-60016.

Keywords:

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏