Primitive orthogonal idempotents for \(R\)-trivial monoids.
A monoid \(S\) is said to be \(R\)-trivial if Green's relation \(\mathcal R\) is equal to the identity relation. The so called weakly ordered monoids were introduced by \textit{M. Schocker} [J. Algebr. Comb. 28, No. 1, 231-234 (2008; Zbl 1175.20054)] in order to generalize simultaneously 0-Hecke monoids and left regular bands. The problem was to find a complete system of orthogonal idempotents for the corresponding monoid algebras. Every weakly ordered monoid is an \(R\)-trivial monoid. It is proved that for finite monoids the inverse proposition is also true. This fact is used to build a recursive formula for a complete system of primitive orthogonal idempotents for any \(R\)-trivial monoid.
scientific article; zbMATH DE number 6029104
scientific article