Algebra Seminar: East -- Semigroups of singular mappings

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

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Speaker: James East (University of Western Sydney) 

Date: Friday 16 September 

Time: 12.05-12.55pm 

Venue: Carslaw 175 

Title: 

Semigroups of singular mappings 

Abstract: 

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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