2024/10/31 by Duchamp, Gérard Henry Edmond, Geloun, Joseph Ben, Tollu, Christophe
#Discrete Mathematics (cs.DM) #FOS: Computer and information sciences
paper · doi:10.48550/arxiv.2410.23731
We show that the algebra of the coloured rook monoid Rn(r), \em i.e. the monoid of n × n matrices with at most one non-zero entry (an r-th root of unity) in each column and row, is the algebra of a finite groupoid, thus is endowed with a C^*-algebra structure. This new perspective uncovers the representation theory of these monoid algebras by making manifest their decomposition in irreducible modules.