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Subspace Semigroups

✍ Scribed by Jan Okniński; Mohan S. Putcha

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
134 KB
Volume
233
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

For a finite dimensional algebra A over an infinite field K, the subspace Ž . Ž . semigroup S S A consists of all subspaces of A with operation V )W s lin VW .

K

Ž .

We describe the structure of S S A , showing in particular that, similarly to any Ž . algebraic linear semigroup, S S A is strongly -regular; we describe its regular elements and regular T T-classes. As the key intermediate step, for an arbitrary Ž . connected algebraic monoid M, we study the semigroup C C M consisting of all irreducible closed subsets with operation X и Y s XY, and we transfer the informa-Ž . Ž . Ž . tion to S S A via the natural onto homomorphism C C A ª S S A . With potential applications in mind, our primary focus in this paper is on the case of the full Ž . matrix algebra A s M K .

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