Centro de Matematica -

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September, 15 - Suzana Mendes-Gonçalves (CMAT-UM)

Given an infinite-dimensional vector space $V$ , we consider the semigroup $GS(m,n)$ consisting of all injective linear $\alpha:V\to V$ for which $codim\, ran\, \alpha=n$ where $\dim V=m\geq n\geq\aleph_0$ . This is a linear version of the well-known Baer-Levi semigroup $BL(p,q)$ defined on an infinite set $X$ where $\vert X\vert=p\geq q\geq\aleph_0$ . Recently, Prof R P Sullivan and I showed that, although the basic properties of $GS(m,n)$ are the same as those of $BL(p,q)$ , the two semigroups are never isomorphic. We also determined all left ideals of $GS(m,n)$ and some of its maximal subsemigroups: in this, we followed previous work on $BL(p,q)$ by Sutov (1966) and Sullivan (1978) as well as Levi and Wood (1984). I will discuss some of that work in this talk.

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