The algebra of binary trees is affine complete
Résumé
A function on an algebra is congruence preserving if, for any congruence, it maps pairs of congruent elements onto pairs of congruent elements. We show that on the algebra of binary trees whose leaves are labeled by letters of an alphabet containing at least three letters, a function is congruence preserving if and only if it is a polynomial function, thus exhibiting the first example of a non commutative and non associative affine complete algebra.
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