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

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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
Pages (from-to)281-299
Number of pages19
Publication statusPublished - Apr 2021

    Research areas

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

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