The quiver of an affine monoid

2020/09/25 by Shahzamanian, M. H., Steinberg, Benjamin · 1 citation
#20M25 #20M30 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2009.12340

Abstract

If R is a finite commutative ring, then the affine monoid of R is the monoid of all affine mappings x↦ ax+b on R. Alternatively, it is the semidirect product of the multiplicative monoid of R with the additive group of R. In this paper we compute the Gabriel quiver of the complex algebra of the affine monoid of any finite commutative ring.

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• Representation theory of monoids consisting of order-preserving functions and order-reversing functions on an n-set

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