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

Henrik Stetkaer*

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

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.

Original languageEnglish
JournalAequationes Mathematicae
Volume95
Issue2
Pages (from-to)281-299
Number of pages19
ISSN0001-9054
DOIs
Publication statusPublished - Apr 2021

Keywords

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

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