Sweedler's duals and Schützenberger's calculus

Gérard H. E. Duchamp (1) , Christophe Tollu (1)

1 LIPN - Laboratoire d'Informatique de Paris-Nord

We describe the problem of Sweedler's duals for bialgebras as essentially characterizing the domain of the transpose of the multiplication. This domain is the set of what could be called ``representative linear forms'' which are the elements of the algebraic dual which are also representative on the multiplicative semigroup of the algebra.

Mots clés: Sweedler's dual; representative functions; automata; semiring; semigroup

Domaines: Combinatoire [math.CO]; Mathématique discrète [cs.DM]; Physique mathématique [math-ph]

Gérard H. E. Duchamp, Christophe Tollu. Sweedler's duals and Schützenberger's calculus. 2007. ⟨hal-00193180v1⟩