Conjugacy classes of Renner monoids

A Note on Renner Monoids

We extend the result obtained in [3] to every Renner monoid: we provide Renner monoids with a monoid presentation and we introduce a length function which extends the Coxeter length function and which behaves nicely.

Conjugacy in Special Monoids

A monoid is special if it is presented by a set of relations of the form r = e. This paper investigates the problem of conjuacy in special monoids. After showing that the different concepts of conjugacy become identical in special monoids, which gives an affirmative answer to an open problem in 171, we prove that the conjugacy problem is decidable for some restricted classes of special monoids....

Deciding conjugacy in sylvester monoids and other homogeneous monoids

Acknowledgements: During the research that led to the this paper, the first author was initially supported by the European Regional Development Fund through the programme  and by the PortugueseGovernment through the  (Fundação para a Ciência e a Tecnologia) under the project -/// and through an  Ciência  fellowship, and later supported by an  Investigador a...

Generalized Conjugacy Classes

Generalized conjugation is the action of a group on its underlying set given by (g, x) 7→ φ(g)xg, where φ : G → G is some fixed endomorphism. Here we study combinatorial properties of the sizes of the orbits of the preceding action. In particular, we reduce the problem to a simpler case if φ has a nontrivial kernel or if it is an inner automorphism, and we give a construction that allows a part...

. Renner Linear Algebraic Monoids SPIN – Monograph – January 12 , 2005