We show that, over an arbitrary field, q-rook monoid algebras are iterated inflations of Iwahori-Hecke algebras, and, in particular, are cellular. Furthermore we give an algebra decomposition which shows a q-rook monoid algebra is Morita equivalent to a direct sum of Iwahori-Hecke algebras. We state some of the consequences for the representation theory of q-rook monoid algebras.

We obtain presentations for the Brauer monoid, the partial analogue of the Brauer monoid, and for the greatest factorizable inverse submonoid of the dual symmetric inverse monoid. In all three cases we apply the same approach, based on the realization of all these monoids as Brauer-type monoids.

We give a new construction of a Hopf algebra defined first by Reading [Rea05] whose bases are indexed by objects belonging to the Baxter combinatorial family (i.e., Baxter permutations, pairs of twin binary trees, etc.). Our construction relies on the definition of the Baxter monoid, analog of the plactic monoid and the sylvester monoid, and on a RobinsonSchensted-like correspondence and insert...

We show that the monoid M2(T) of 2 × 2 tropical matrices is a regular semigroup satisfying the semigroup identity A2B4A2A2B2A2B4A2 =A2B4A2B2A2A2B4A2. Studying reduced identities for subsemigroups of M2(T), and introducing a faithful semigroup representation for the bicyclic monoid by 2 × 2 tropical matrices, we reprove Adjan’s identity for the bicyclic monoid in a much simpler way.

Informally, a homotopy monoid is a monoid-like structure in which properties such as associativity only hold ‘up to homotopy’ in some consistent way. This short paper comprises a rigorous definition of homotopy monoid and a brief analysis of some examples. It is a much-abbreviated version of the paper ‘Homotopy Algebras for Operads’ (math.QA/0002180), and does not assume any knowledge of operads.

We prove that any affine algebraic monoid can be obtained as the endomorphisms’ monoid of a finite-dimensional (nonassociative) algebra.

Let X∗ be a free monoid over an alphabet X and W be a finite language over X. Let S(W ) be the Rees quotient X∗/I(W ), where I(W ) is the ideal of X∗ consisting of all elements of X∗ that are not subwords of W . Then S(W ) is a finite monoid with zero and is called the discrete syntactic monoid of W . W is called finitely based if the monoid S(W ) is finitely based. In this paper, we give some ...

The aim of this paper is to investigate whether the class of automaton semigroups is closed under certain semigroup constructions. We prove that the free product of two automaton semigroups that contain left identities is again an automaton semigroup. We also show that the class of automaton semigroups is closed under the combined operation of ‘free product followed by adjoining an identity’. W...

The goal of the article is to define the concept of monoid. In the preliminary section we introduce the notion of some properties of binary operations. The second section is concerning with structures with a set and a binary operation on this set: there is introduced the notion corresponding to the notion of some properties of binary operations and there are shown some useful clusters. Next, we...

The non-parametric, or re-sampling, bootstrap for a single unstructured sample corresponds to the algebraic operation of monoid composition, with a uniform distribution on the monoid. With this interpretation, the notion of re-sampling can be extended to designs having a certain group-invariance property. Two types of exchangeable array structures are considered in some detail, namely the one-w...