The Newtonian divided-di¤erence operators generate the nil-Coxeter algebra and semigroup. A bijective correspondence between the nil-Coxeter semigroup and the symmetric group is used to provide braid-like diagrams for the former, and corresponding Reidemeister-type moves for the relations. Conditions are given for similar relations to hold in a skew group ring. Interesting extensions of the nil...

We classify actions of finite groups on some class of C*-algebras with the Rokhlin property in terms of the Cuntz semigroup. An obstruction is obtained for the Cuntz semigroup of a C*-algebra allowing such an action. We also classify certain inductive limit actions of finite groups on a class of C*-algebras containing AI-algebras. This classification is done via the equivariant Cuntz semigroup.

First, we introduce the concept of intuitionistic fuzzy group congruenceand we obtain the characterizations of intuitionistic fuzzy group congruenceson an inverse semigroup and a T^{*}-pure semigroup, respectively. Also,we study some properties of intuitionistic fuzzy group congruence. Next, weintroduce the notion of intuitionistic fuzzy semilattice congruence and we givethe characterization of...

‎generalizing the notion of character amenability for banach‎ ‎algebras‎, ‎we study the concept of $varphi$-connes amenability of‎ ‎a dual banach algebra $mathcal{a}$ with predual $mathcal{a}_*$‎, ‎where $varphi$ is a homomorphism from $mathcal{a}$ onto $bbb c$‎ ‎that lies in $mathcal{a}_*$‎. ‎several characterizations of‎ ‎$varphi$-connes amenability are given‎. ‎we also prove that the‎ ‎follo...

The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. In this paper, we investigate the concept of restricted positive definite functions and their relation with restricted representations of an inverse semigroup. We also introduce the restricted Fourier ...

The five-element Brandt semigroup B2 and its four-element subsemigroup B0, obtained by omitting one nonidempotent, have played key roles in the study of varieties of semigroups. Regarded in that fashion, they have long been known to be finitely based. The semigroup B2 carries the natural structure of an inverse semigroup. Regarded as such, in the signature {·,−1 }, it is also finitely based. It...

We study the asymptotic behaviour of a finitely presented Rees quotient S = Inv〈A | ci = 0 (i = 1, . . . , k) 〉 of a free inverse semigroup over a finite alphabet A. It is shown that if the semigroup S has polynomial growth then S is monogenic (with zero) or k ≥ 3. The three relator case is fully characterised, yielding a sequence of two-generated three-relator semigroups whose Gelfand-Kirillov...

Inverse semigroups generalise both groups and semilattices, and describe partial symmetries just as groups do for total symmetries; they also arise naturally in appropriately rich categories, essentially as monoids of partial automorphisms. Analogy with the group case suggests that the use of inverse semigroups will be assisted by the development of a workable representation theory. Moreover th...

In this paper, we introduce the concept of a wide tensor category which is a special class of a tensor category initiated by the inverse braid monoids recently investigated by Easdown and Lavers [The Inverse BraidMonoid,Adv. inMath. 186 (2004) 438–455]. The inverse braid monoids IBn is an inverse monoid which behaves as the symmetric inverse semigroup so that the braid group Bn can be regarded ...