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Some recent research on transformation semigroups

Resumo:  During the last decade or so, there has been considerable interest in the algebraic properties of transformations of sets vis-à-vis those of linear transformations of a vector space. Many years ago, following some of Gould?s ideas, Fountain and Lewin (1992-1993) used ?independence algebras? to unify the two areas. But they had to impose some restrictions on their algebras in order to explain very specific differences between the two areas. Hence, as more differences were found, it became harder to explain them. So, nowadays many people continue to work in one (or both) of these
areas without using algebras of any kind.

Although these differences are usually subtle, they are substantial. Also, surprisingly, the results for vector spaces are often more complete and more elegant than the corresponding ones for sets (also the proofs are completely different). In this talk, I will discuss one or more results of this kind for the following topics.

--skew idempotents, by Blyth & Almeida Santos (2006), Changphas & Sullivan (to appear)

--restricted ranges, by Sommanee & Sanwong (2007), Sullivan (2008)

--BQ-property, by Kemprasit (2001-2003), Sullivan (2009)
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