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Pseudovarieties generated by Brauer type monoids
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Karl Auinger
Published/Copyright:
August 19, 2011
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.
Received: 2010-11-08
Revised: 2011-06-06
Published Online: 2011-08-19
Published in Print: 2014-01-01
© 2014 by Walter de Gruyter Berlin Boston
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- Pseudovarieties generated by Brauer type monoids
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Keywords for this article
Brauer monoid;
partition
monoid;
pseudovariety;
wreath product;
Krohn–Rhodes theory
Articles in the same Issue
- Masthead
- Pseudovarieties generated by Brauer type monoids
- On some arithmetic properties of Siegel functions (II)
- Perfect vector alignment of the vorticity and the vortex stretching is one forever
- Frobenius groups of automorphisms and their fixed points
- Schubert calculus and the Hopf algebra structures of exceptional Lie groups
- The sovability of norm, bilinear and quadratic equations over finite fields via spectra of graphs
- Periodicity in the stable representation theory of crystallographic groups
- Sums of Fourier coefficients of a Maass form for SL3(ℤ) twisted by exponential functions
- The rational classification of links of codimension > 2
- On the classifying space for proper actions of groups with cyclic torsion
- Turán determinants of Bessel functions
