The small dimension lemma and d'Alembert's equation on semigroups

被引：11

作者：

Stetkaer, Henrik ^{[1
]}

机构：

[1] Aarhus Univ, Inst Math, Ny Munkegade 118, DK-8000 Aarhus C, Denmark

来源：

AEQUATIONES MATHEMATICAE | 2021年 / 95卷 / 02期

关键词：

Functional equation; d'Alembert; involution; representation; semigroup;

D O I：

10.1007/s00010-020-00746-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive an algebraic version over an algebraically closed field k with characteristic not equal 2 of Yang's Small Dimension Lemma. With its help we describe the k-valued solutions of d'Alembert's functional equation on semigroups S in terms of multiplicative functions and irreducible, 2-dimensional representations of S.

引用

页码：281 / 299

页数：19

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