Presentations for rook partition monoids and algebras and their singular ideals

2016/06/02 by East, James · 1 citation
#FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1606.00563

Abstract

We obtain several presentations by generators and relations for the rook partition monoids and algebras, as well as their singular ideals. Among other results, we also calculate the minimal sizes of generating sets (some of our presentations use such minimal-size generating sets), and show that the singular part of the rook partition monoid is generated by its idempotents.

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• Presentations for semigroups of full-domain partitions

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