The system of idempotents and the lattice of \({\mathcal J}\)-classes of reductive algebraic monoids
The authors determine the lattice of \({\mathcal J}\)-classes of a regular algebraic monoid, which has only one non-zero minimal \({\mathcal J}\)-class. There are results on the structure of the set of idempotents of a regular algebraic monoid. Many structural questions are reduced to determining the finite lattice \({\mathcal U}=G\setminus M/G\) of \({\mathcal J}\)-classes, where M is a regular algebraic monoid and G is its unit group. It becomes clear that \({\mathcal U}\) is an important semigrouptheoretic link between irreducible representations of G and the Tits building \(\Delta_ G\) of G.
scientific article; zbMATH DE number 4110954
scientific article