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

Henrik Stetkaer*

*Corresponding author af dette arbejde

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Abstract

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.

OriginalsprogEngelsk
TidsskriftAequationes Mathematicae
Vol/bind95
Nummer2
Sider (fra-til)281-299
Antal sider19
ISSN0001-9054
DOI
StatusUdgivet - apr. 2021

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