University of Western Sydney

School of Computing, Engineering and Mathematics Seminars

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Semigroups of singular transformations


Speaker: James East

Affiliation: University of Western Sydney

Time: Monday 08/08/2011 from 14:00 to 15:00

Venue: Access Grid UWS. Presented from Parramatta (EB.1.32), accessible from Campbelltown (26.1.50) and Penrith (Y239).

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 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.

Biography: James is a member of the Centre for Research in Mathematics and a lecturer with the School of Computing, Engineering and Mathematics.

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