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 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.

A differential Azumaya algebra, and in particular a differential matrix algebra, over a differential field K with constants C is trivialized by a Picard–Vessiot (differential Galois) extension E. This yields a bijection between isomorphism classes of differential algebras and Picard–Vessiot cocycles Z(G(E/K), PGLn(C)) which cobound in Z (G(E/K), PGLn(E)).

We exploit the Fedosov-Weinstein-Xu (FWX) resolution proposed in q-alg/9709043 to establish an isomorphism between the ring of Hochschild cohomology of the quantum algebra of functions on a symplectic manifold M and the ring H(M,C((~))) of De Rham cohomology of M with the coefficient field C((~)) without making use of any version of formality theorem. We also show that the Gerstenhaber bracket ...

We investigate conditions on a graph C∗-algebra for the existence of a faithful semifinite trace. Using such a trace and the natural gauge action of the circle on the graph algebra, we construct a smooth (1,∞)-summable semfinite spectral triple. The local index theorem allows us to compute the pairing with K-theory. This produces invariants in the K-theory of the fixed point algebra, and these ...

An amorphic association scheme has the property that any of its fusion is also an association scheme. In this paper we generalize the property to be amorphic to an arbitrary C-algebra and prove that any amorphic C-algebra is determined up to isomorphism by the multiset of its degrees and an additional integer equal ±1. Moreover, we show that any amorphic C-algebra with rational structure consta...

An amorphic association scheme has the property that any of its fusion is also an association scheme. In this paper we generalize the property to be amorphic to an arbitrary C-algebra and prove that any amorphic C-algebra is determined up to isomorphism by the multiset of its degrees and an additional integer equal ±1. Moreover, we show that any amorphic C-algebra with rational structure consta...

Let τ be an invertible skew pairing on (B,H), where B and H are Hopf algebras in a symmetric monoidal category C with (co)equalizers. Assume that H is quasitriangular. Then we obtain a new algebra structure such that B is a Hopf algebra in the braided category HYD and there exists a Hopf algebra isomorphism w : B∞H → B τH in C, where B∞H is a Hopf algebra with (co)algebra structure the smash (c...