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
收藏
页码：281 / 299
页数：19
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