2011/08/14 by V. N. Krishnachandran, Krishnachandran, V. N.
Mathematics · #20M17 #20M32 #58A05 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #math.DG #msc:20M17 #msc:20M32 #msc:58A05
paper · pdf · doi:10.48550/arxiv.1108.2878
12 pages
arxiv created 2011/08/14 · openalex publication_date 2011/08/14 · arxiv updated 2011/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.