‎Let $Omega$ be a class of unital‎ ‎$C^*$-algebras‎. ‎We introduce the notion of a local tracial $Omega$-algebra‎. ‎Let $A$ be an $alpha$-simple unital local tracial $Omega$-algebra‎. ‎Suppose that $alpha:Gto $Aut($A$) is an action of a finite group $G$ on $A$‎ ‎which has a certain non-simple tracial Rokhlin property‎. ‎Then the crossed product algebra‎ ‎$C^*(G,A,alpha)$ is a unital local traci...

It is known that the generator of a strictly continuous one parameter unitary group in the multiplier algebra of a C∗ -algebra is affiliated to that C∗ -algebra . We show that under natural non degeneracy conditions, this self adjoint unbounded operator lies indeed in the (unbounded) multiplier algebra of the Pedersen’s ideal of the C∗ -algebra .

We consider three Lie algebras: Der C((t)), the Lie algebra of all derivations on the algebra C((t)) of formal Laurent series; the Lie algebra of all differential operators on C((t)); and the Lie algebra of all differential operators on C((t)) ⊗ Cn. We prove that each of these Lie algebras has an essentially unique nontrivial central extension. The Lie algebra of all derivations on the Laurent ...

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An action of Z by automorphisms of a k-graph induces an action of Z by automorphisms of the corresponding k-graph C∗-algebra. We show how to construct a (k + l)-graph whose C∗-algebra coincides with the crossed product of the original k-graph C∗-algebra by Z. We then investigate the structure of the crossed-product C∗-algebra.

We introduce a notion of covering dimension for Cuntz semigroups C⁎-algebras. This is always bounded by the nuclear C⁎-algebra, and subhomogeneous C⁎-algebras both dimensions agree. Z-stable have at most one. Further, semigroup simple, C⁎-algebra zero-dimensional if only has real rank zero or stably projectionless.