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

Henrik Stetkaer

doi:10.1007/s00010-020-00746-x

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

^*Corresponding author for this work

Department of Mathematics

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Abstract

We derive an algebraic version over an algebraically closed field k with characteristic ≠ 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.

Original language	English
Journal	Aequationes Mathematicae
Volume	95
Issue	2
Pages (from-to)	281-299
Number of pages	19
ISSN	0001-9054
DOIs	https://doi.org/10.1007/s00010-020-00746-x
Publication status	Published - Apr 2021

Keywords

Functional equation
d'Alembert
involution
representation
semigroup

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AB - We derive an algebraic version over an algebraically closed field k with characteristic ≠ 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.

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KW - d'Alembert

KW - involution

KW - representation

KW - semigroup

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

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