Abstract
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.
Original language | English |
---|---|
Journal | Aequationes Mathematicae |
Volume | 95 |
Issue | 2 |
Pages (from-to) | 281-299 |
Number of pages | 19 |
ISSN | 0001-9054 |
DOIs | |
Publication status | Published - Apr 2021 |
Keywords
- Functional equation
- d'Alembert
- involution
- representation
- semigroup