Pseudo-Euclidean Hurwitz Pairs and Generalized Fueter Equations
Pseudo-Euclidean Hurwitz Pairs and Generalized Fueter Equations
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伪欧几里得 Hurwitz 对和广义 Fueter 方程
DOI：
10.1007/978-94-009-4728-3_3
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发表时间：
1986
期刊：
影响因子：
--
通讯作者：
J. Rembieliński
中科院分区：
文献类型：
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作者：
J. Ławrynowicz;J. Rembieliński
在[15]中，作者用Clifford代数的语言重新阐述了Hurwitz问题[10]，即找到所有正整数对（n，p）和所有系统，使得双线性形式的集合满足条件。他们引入了两个实酉向量空间V和S的Hurwitz对的概念。他们研究了这些对对诱导辛分解的依赖性，并以自然的方式得出了复杂的几何诱导通过给定的辛分解，在 S 中具有明显的固定方向，引入了一种各向异性。在这个方向上的进一步研究已在[11-13, 16]中进行。如果所讨论的向量空间V和S配备有具有标准属性的非简并伪欧几里得实标量积，则当前的研究与所引用的结构的类似物相关。这使得作者能够介绍和研究一些广义的 Fueter 方程，扩展或改进 F. Brackx、R. Delanghe、V. Souček、A. Vaz Ferreira 等人关于全纯的某些结果。
In [15] the authors have reformulated, in the language of Clifford algebras, theHurwitz problem[10] of finding all the pairs of positive integers (n, p) and all the systemssuch that the set of bilinear formssatisfies the conditionThey have introduced the notion of theHurwitz pairof two real unitary vector spaces V and S. They have studied the dependence of these pairs on induced symplectic decomposition and arrived in a natural way at acomplex geometry induced by a given symplectic decompositionwith a distinguished fixed direction in S, that introduced a kind of anisotropy. Further investigations in this direction have been done in [11–13, 16].The present research is connected with an analogue of the quoted construction if the vector spaces V and S in question are equipped withnon-degenerate pseudo-euclidean real scalar productswith standard properties. This enables the authors to introduce and study somegeneralized Fueter equations, extending or improving certain results on holomorphy due to F. Brackx, R. Delanghe, V. Souček, A. Vaz Ferreira, and others.