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

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The small dimension lemma and d'Alembert's equation on semigroups. / Stetkaer, Henrik.

In: Aequationes Mathematicae, Vol. 95, No. 2, 04.2021, p. 281-299.

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Stetkaer, Henrik. / The small dimension lemma and d'Alembert's equation on semigroups. In: Aequationes Mathematicae. 2021 ; Vol. 95, No. 2. pp. 281-299.

Bibtex

@article{3c2a2ff722814db4ac538471e1ecf197,
title = "The small dimension lemma and d'Alembert's equation on semigroups",
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.",
keywords = "Functional equation, d'Alembert, involution, representation, semigroup",
author = "Henrik Stetkaer",
year = "2021",
month = apr,
doi = "10.1007/s00010-020-00746-x",
language = "English",
volume = "95",
pages = "281--299",
journal = "Aequationes Mathematicae",
issn = "0001-9054",
publisher = "Springer Basel AG",
number = "2",

}

RIS

TY - JOUR

T1 - The small dimension lemma and d'Alembert's equation on semigroups

AU - Stetkaer, Henrik

PY - 2021/4

Y1 - 2021/4

N2 - 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.

AB - 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.

KW - Functional equation

KW - d'Alembert

KW - involution

KW - representation

KW - semigroup

U2 - 10.1007/s00010-020-00746-x

DO - 10.1007/s00010-020-00746-x

M3 - Journal article

VL - 95

SP - 281

EP - 299

JO - Aequationes Mathematicae

JF - Aequationes Mathematicae

SN - 0001-9054

IS - 2

ER -