A representation of the coalgebra of derivations for smooth spaces
Let be a field. The generalized Leibniz rule for higher derivations suggests the definition of a coalgebra for any positive integer . This is spanned over by , and has comultiplication and counit defined by and (Kronecker’s delta) for any . This note presents a representation of the coalgebra by using smooth spaces and a procedure of microlocalization. The author gives an interpretation of this result following the principles of the quantum theory of geometric spaces.