Plastic algebra of rank 3

The structure of the algebra K[M] of the plactic monoid M of rank 3 over a field K is studied. The minimal prime ideals of K[M] are described. There are only two such ideals and each of them is a principal ideal determined by a homogeneous congruence on M. Moreover, in case K is uncountable and algebraically closed, the left and right primitive spectrum and the corresponding irreducible representations of the algebra K[M] are described. All these representations are monomial. As an application, a new proof of the semiprimitivity of K[M] is given.

Jaar van publicatie:2012

Trefwoorden:plastic algebra