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Orbit Structure Of Finite And Reductive Monoids, Zhuo Li

Digitized Theses

A reductive monoid is an algebraic monoid with a reductive unit group. We introduce a new class of reductive monoids, $({\cal T}, \sigma)$-irreducible monoids. Generally, we have the question of finding the orbits of the unit group of a reductive monoid acting on both sides of the monoid. Putcha and Renner give a recipe to determine the orbits for ${\cal T}$-irreducible monoids. Motivated by their construction of finite reductive monoids, the concept of (${\cal T}, \sigma)$-irreducible monoid arises naturally.

We obtain that the ${\cal T}$-irreducible monoids turn out to be a special class of the $({\cal T}, \sigma)$-irreducible monoids. We …