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The Renner Monoids And Cell Decompositions Of The Classical Algebraic Monoids, Zhenheng Li
The Renner Monoids And Cell Decompositions Of The Classical Algebraic Monoids, Zhenheng Li
Digitized Theses
The Renner monoids, cross section lattices and cell decompositions of the classical algebraic monoids are studied.
The Renner monoid is extremely important in the theory of reductive algebraic monoids. It is well know that the Renner monoid [Special characters omitted.] of Mn (K ) is the monoid of all zero-one matrices which have at most one entry equal to one in each row and column, i.e., [Special characters omitted.] consists of injective partial maps on a set of n elements. We obtain that the Renner monoids of the symplectic algebraic monoids and special orthogonal algebraic monoids turn out …
Orbit Structure Of Finite And Reductive Monoids, Zhuo Li
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 …