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

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 ≠ 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 ≠ 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

UR - http://www.scopus.com/inward/record.url?scp=85089658648&partnerID=8YFLogxK

U2 - 10.1007/s00010-020-00746-x

DO - 10.1007/s00010-020-00746-x

M3 - Journal article

SN - 0001-9054

VL - 95

SP - 281

EP - 299

JO - Aequationes Mathematicae

JF - Aequationes Mathematicae

IS - 2

ER -