On idempotent DD-norms

Replacing the spectral measure by a random vector Z allows the representation of a max-stable distribution on RdRd with standard negative margins via a norm, called DD-norm  , whose generator is Z. The set of DD-norms can be equipped with a commutative multiplication type operation, making it a semigroup with an identity element. This multiplication leads to idempotent DD-norms. We characterize the set of idempotent DD-norms. Iterating the multiplication provides a track of DD-norms, whose limit exists and is again a DD-norm. If this iteration is repeatedly done on the same DD-norm, then the limit of the track is idempotent.