SMS scnews item created by Anne Thomas at Fri 9 Sep 2011 1356
Type: Seminar
Distribution: World
Expiry: 16 Sep 2011
Calendar1: 16 Sep 2011 1205-1255
CalLoc1: Carslaw 175
Auth: athomas(.pmstaff;2039.2002)

Algebra Seminar: East -- Semigroups of singular mappings

There will be an Algebra Seminar by James East next Friday 16 September.  


Speaker: James East (University of Western Sydney) 

Date: Friday 16 September 

Time: 12.05-12.55pm 

Venue: Carslaw 175 


Semigroups of singular mappings 


John Howie showed in 1966 that any non-bijective function from a finite set to itself
can be obtained by composing a number of idempotent functions.  In semigroup theoretic
terms, this says that the singular part of a finite transformation semigroup is
generated by its idempotents.  I’ll present a set of defining relations for this
singular subsemigroup with respect to the generating set consisting of all corank 1
idempotents.  Along the way, I’ll also discuss some other extensions of Howie’s results
in the context of (some of) partial transformation semigroups, Brauer monoids, partition
monoids, semigroups of integer matrices, and semigroups of transformations of various
kinds of spaces.  If time permits, I’ll say something about the infinite case.  


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