Manifold structures in regular irreducible algebraic monoids

Details Manifold structures in regular irreducible algebraic monoids Manifold structures in regular irreducible algebraic monoids

2011-08-14

arxiv.org/abs/1108.2878v1

Mathematics

Differential Geometry

12 pages

Scientific paper

In this paper we study regular irreducible algebraic monoids over $\fldc$ equipped with the euclidean topology. It is shown that, in such monoids, the Green classes and the spaces of idempotents in the Green classes all have natural manifold structures. The interactions of these manifold structures and the semigroup structures in these monoids have been investigated. Relations between these manifolds and Grassmann manifolds have been established. A generalisation of a result on the dimension of the manifold of rank $k$ idempotents in the semigroup of linear endomorphisms over $\fldc$ has been proved.

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