Abstract
It is proved that the series of all Brauer monoids generates the pseudovariety of all finite monoids while the series of their aperiodic analogues, the Jones monoids (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 form a generating series for the pseudovariety of all finite aperiodic monoids can be viewed as solution of an old problem popularized by J.-É. Pin. For the latter, the relationship between the Jones monoids and the monoids of order preserving mappings of a chain of length n is investigated.
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