In this paper, we first define the pre-Lie family algebra associated to a dendriform in case of commutative semigroup. Then construct via typed decorated rooted trees, and prove freeness algebra. We also operad terms labeled obtain that algebras is isomorphic which generalizes result Chapoton Livernet. end, Zinbiel pre-Poisson generalize results Aguiar.

An inverse semigroup is a semigroup S such that for each x e S there exists a unique inverse x~ & S such that both xx~x=x and x~xx~=x~\ This condition is equivalent to S both being (von Neumann) regular and having all idempotents commute. The classic example of such a semigroup is the symmetric inverse semigroup Ix of all partial bijections on a set X under the standard composition of partial f...

This paper examines actions of right LCM semigroups by endomorphisms C*-algebras that encode an additional structure the semigroup. We define contractive covariant representations for these semigroup dynamical systems and prove a generalized Stinespring's dilation theorem showing can be dilated if only map on C*-algebra is unital completely positive. generalizes earlier results about dilations ...

Let M be a finite monoid of Lie type (these are the finite analogues of linear algebraic monoids) with group of units G . The multiplicative semigroup ^AfF), where F is a finite field, is a particular example. Using HarishChandra's theory of cuspidal representations of finite groups of Lie type, we show that every complex representation of M is completely reducible. Using this we characterize t...

The results in this paper were motivated by the case when the inverse semigroup is the McAlister monoid MX on a set X. In [1] we considered some very large convolution algebras on MX , including some C ∗-algebras. Our main focus in [1] was deciding on the primitivity of the algebras, and one key tool was the use of generalized Rukolaine idempotents. To define these very large convolution algebr...

If R is a 2-sided fir (free ideal ring) with no non-trivial right invariant elements, we shall find that the non-zero 2-sided ideals of R, under the usual multiplication of ideals, form a free semigroup with 1. In particular, this holds when R is a free associative algebra over a field. (We also consider the operations of multiplying right ideals by 2-sided ideals to get right ideals, 2-sided i...

Let S be a (discrete) semigroup, and let ` (S) be the Banach algebra which is the semigroup algebra of S. We shall study the structure of this Banach algebra and of its second dual. We shall determine exactly when ` (S) is amenable as a Banach algebra, and shall discuss its amenability constant, showing that there are ‘forbidden values’ for this constant. The second dual of ` (S) is the Banach ...

An inflation of an algebra is formed by adding a set of new elements to each element in the original or base algebra, with the stipulation that in forming products each new element behaves exactly like the element in the base algebra to which it is attached. Clarke and Monzo have defined the generalized inflation of a semigroup, in which a set of new elements is again added to each base element...

We provide inverse semigroup and groupoid models for the Toeplitz and Cuntz-Krieger algebras of finitely aligned higher-rank graphs. Using these models, we prove a uniqueness theorem for the Cuntz-Krieger algebra.