Pseudovarieties generated by Brauer type monoids

It is proved that the series of all Brauer monoids B-n generates the pseudovariety of all finite monoids while the series of their aperiodic analogues, the Jones monoids J(n) (also called Temperly-Lieb monoids), generates the pseudovariety of all finite aperiodic monoids. The proof is based on the analysis of wreath product decomposition and Krohn-Rhodes theory. The fact that the Jones monoids J(n) form a generating series for the pseudovariety of all finite aperiodic monoids can be viewed as solution of an old problem popularized by J.-E. Pin. For the latter, the relationship between the Jones monoids J(n) and the monoids O-n of order preserving mappings of a chain of length n is investigated.