We introduce the growth rank of a C∗-algebra — a (N∪ {∞})-valued invariant whose minimal instance is equivalent to the condition that an algebra absorbs the Jiang-Su algebra Z tensorially — and prove that its range is exhausted by simple, nuclear C∗-algebras. As consequences we obtain a well developed theory of dimension growth for approximately homogeneous (AH) C∗-algebras, establish the exist...

We investigate C∗-algebras associated with row-finite topological higherrank graphs with no source, which are based on product system C∗-algebras. We prove the Cuntz-Krieger uniqueness theorem, and provide the condition of simplicity and purely infiniteness of our algebras. We give examples of non-discrete topological higher-rank graphs whose C∗-algebras contain Cuntz’s ax + b-semigroup C∗-alge...

In this article, we study the non-Newtonian version of C∗−algebras. Further, generalize some results which hold for classical We also discuss illustrative examples to show accuracy and effectiveness new findings. If take identity function I instead generators α β in construction set C(N), then C∗−algebras turn into C∗−algebras, so our are stronger than knowledge facts most existing literature.

A subalgebra B of a Leibniz algebra L is called weak c-ideal if there subideal C such that L=B+C and B∩C⊆BL where BL the largest ideal contained in B. This analogous to concept weakly c-normal subgroup, which has been studied by number authors. We obtain some properties c-ideals use them give characterizations solvable supersolvable algebras generalizing previous results for Lie algebras. note ...

We describe a class of C *-algebras which simultaneously generalise the ul-tragraph algebras of Tomforde and the shift space C *-algebras of Matsumoto. In doing so we shed some new light on the different C *-algebras that may be associated to a shift space. Finally, we show how to associate a simple C *-algebra to an irreducible sofic shift.

We show that Rieffel’s functor sends covariant C(T )-algebras in C(T )-algebras and covariant continuous fields of C∗-algebras in continuous fields of C∗-algebras. We use this to prove spectral continuity results for families of Rieffel-type pseudodifferential operators.

We prove that a number of classes of separable unital C*-algebras are closed under crossed products by finite group actions with the Rokhlin property, including: • AI algebras, AT algebras, and related classes characterized by direct limit decompositions using semiprojective building blocks. • Simple unital AH algebras with slow dimension growth and real rank zero. • C*-algebras with real rank ...

Many important C∗-algebras, such as AF-algebras, Cuntz-Krieger algebras, graph algebras and foliation C∗-algebras, are the C∗-algebras of r-discrete groupoids. These C∗-algebras are often associated with inverse semigroups through the C∗-algebra of the inverse semigroup [HR90] or through a crossed product construction as in Kumjian’s localization [Kum84]. Nica [Nic94] connects groupoid C∗-algeb...

in this paper, we generalize some results from hilbert c*-modules to pro-c*-algebra case. we also give a new proof of the known result that l2(a) is ahilbert module over a pro-c*-algebra a.