The quiver of an affine monoid

If $R$ is a finite commutative ring, then the affine monoid of $R$ is the monoid of all affine mappings $x\mapsto ax+b$ on $R$. Alternatively, it is the semidirect product of the multiplicative monoid of $R$ with the additive group of $R$. Ayyer and Steinberg studied Markov chains coming from random applications of $ax+b$ mappings on $R$ using the representation theory of the affine monoid $Aff(R)$ of all such maps. They described the simple $\mathbb{C}Aff(R)$-modules. In this work, we compute the Gabriel quiver of the complex algebra of the affine monoid of any finite commutative ring. This is joint work with B. Steinberg.

Date and Venue

Start Date
Venue
Online Zoom meeting
End Date

Speaker

M. Hossein Shahzamanian

(FCUP-CMUP)

Area

Semigroups, Automata and Languages