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

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Abstract

We derive an algebraic version over an algebraically closed field k with characteristic \(\ne 2\) 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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  1. Institute of Mathematics, Aarhus University, Ny Munkegade 118, 8000, Aarhus C, Denmark

    Henrik Stetkær

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  1. Henrik Stetkær
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Correspondence to Henrik Stetkær.

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Stetkær, H. The small dimension lemma and d’Alembert’s equation on semigroups. Aequat. Math. 95, 281–299 (2021). https://doi.org/10.1007/s00010-020-00746-x

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  • DOI: https://doi.org/10.1007/s00010-020-00746-x

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