Motivated by recent results of A. Klyachko, we construct a probability preserving, isometric isomorphism from the Banach algebra Mb(SL(d,C)‖SU(d)) of all SU(d)-biinvariant bounded signed measures on SL(d,C) to some Banach subalgebra of the Banach algebra of all bounded signed measures on the Euclidean space of all Hermitian d × d-matrices with trace 0. This isomorphism leads to strong limit the...

We establish axiomatic characterizations of K-theory and KK-theory for real C*-algebras. In particular, let F be an abelian group-valued functor on separable real C*-algebras. We prove that if F is homotopy invariant, stable, and split exact, then F factors through the category KK. Also, if F is homotopy invariant, stable, half exact, continuous, and satisfies an appropriate dimension axiom, th...

Abstract We show that every graded ideal of a Leavitt path algebra is isomorphic to algebra. It known I the graph, as generalised hedgehog which defined based on certain sets vertices uniquely determined by . However, this isomorphism may not be graded. replacing short ‘spines’ graph with possibly fewer, but then necessarily longer spines, we obtain (which call porcupine graph) whose Our proof ...

We introduce stabilised property $\Gamma$, a $\mathrm {C}^*$-algebraic variant of $\Gamma$ which is invariant under stable isomorphism. then show that simple separable nuclear {C}^*$-algebras with and {Cu}(A) \cong \mathrm {Cu}(A \otimes \mathcal {Z})$ absorb the Jiang-Su algebra $\mathcal {Z}$ tensorially.

We give a simple proof of an isomorphism between two C[t]-modules corresponding to bivariate polynomial H with nondegenerate highest homogeneous part: the module of relative cohomologies Λ 2 /dH ∧ Λ 1 and the module of Abelian integrals. Using this isomorphism, we prove existence and deduce some properties of the corresponding Picard-Fuchs system.

A functor G : C → D is said to preserve limits of a diagram D : I → C if it sends any limiting cone from x to D to a limiting cone from G(x) to G◦D. When G preserves limits of a diagram D this entails directly that there is an isomorphism G(lim ←−ID) ∼= lim ←−I(G ◦D) between objects. In general, such an isomorphism alone is not sufficient to ensure that G preserves limits. This paper shows how,...

We describe a method for associating some non-self-adjoint algebras to MauldinWilliams graphs and we study the Morita equivalence and isomorphism of these algebras. We also investigate the relationship between the Morita equivalence and isomorphism class of the C∗-correspondences associated with Mauldin-Williams graphs and the dynamical properties of the Mauldin-Williams graphs.

We consider presentations that were derived in [3] for the interval groups associated with proper quasi-Coxeter elements of Coxeter group W(Dn). use combinatorial methods to derive alternative groups, and these new show a element W(Dn) cannot be isomorphic Artin type Dn. While specific problems we solve arise from study their solution provides an illustration how techniques indicated by computa...