A new algorithm for computing idempotents of Rtrivial monoids
Abstract
The authors of [Primitive orthogonal idempotents for Rtrivial monoids, Journal of Algebra] provide an algorithm for finding a complete system of primitive orthogonal idempotents for CM, where M is any finite Rtrivial monoid. Their method relies on a technical result stating that Rtrivial monoids are equivalent to socalled weakly ordered monoids. We provide an alternative algorithm, based only on the simple observation that an Rtrivial monoid may be realised by upper triangular matrices. This approach is inspired by results in the field of coupled cell network dynamical systems, where Ltrivial monoids (the opposite notion) correspond to socalled feedforward networks. We also show that our algorithm only has to be performed for ZM, after which a complete system of primitive orthogonal idempotents may be obtained for RM, where R is any ring with a known complete system of primitive orthogonal idempotents. In particular, the algorithm works if R is any field.
 Publication:

arXiv eprints
 Pub Date:
 June 2019
 DOI:
 10.48550/arXiv.1906.02844
 arXiv:
 arXiv:1906.02844
 Bibcode:
 2019arXiv190602844N
 Keywords:

 Mathematics  Representation Theory