Abstract. We consider a class of C-algebras associated to one parameter continuous tensor product systems of Hilbert modules, which can be viewed as continuous counterparts of Pimsner’s Toeplitz algebras. By exhibiting a homotopy of quasihomomorphisms, we prove that those algebras are K-contractible. One special case is closely related to the Rieffel-Wiener-Hopf extension of a crossed product b...

An ω-tree-automatic structure is a relational structure whose domain and relations are accepted by Muller or Rabin tree automata. We investigate in this paper the isomorphism problem for ω-tree-automatic structures. We prove first that the isomorphism relation for ω-treeautomatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative gro...

We construct a numeric algorithm for completing the proof of conjecture asserting that all deformed preprojective algebras generalized Dynkin type are periodic. In particular, we obtain an algorithmic procedure showing non-trivial types E7 and E8 exist only in characteristic 2. As consequence, show E6, periodic classification such algebras, up to algebra isomorphism. do it by reduction solution...

We introduce a new spectral sequence called the p-chain spectral sequence which converges to the (co-)homology of a contravariant C-space with coefficients in a covariant C-spectrum for a small category C. It is different from the corresponding Atiyah-Hirzebruch type spectral sequence. It can be used in combination with the Isomorphism Conjectures of Baum-Connes and Farrell-Jones to compute alg...

Let Γ be a group of type rotating automorphisms of an affine building B of type Ã2. If Γ acts freely on the vertices of B with finitely many orbits, and if Ω is the (maximal) boundary of B, then C(Ω) ⋊ Γ is a p.i.s.u.n. C∗-algebra. This algebra has a structure theory analogous to that of a simple Cuntz-Krieger algebra and is the motivation for a theory of higher rank CuntzKrieger algebras, whic...

Let L be a 1-reduced simplicial set. Let G(−) and C(−) be the Kan loop group and normalized chain functors respectively. The explicit, natural twisting cochain tL : CL → C(GL) of Szczarba [16] determines a natural morphism of chain algebras θL : ΩCL → C(GL) that induces an isomorphism in homology, since CL is 1-connected. Here ΩCL is the cobar construction [1]. The coassociative, counital diago...

We work on the classification of isomorphism classes finitely generated projective modules over C*-algebras $C\left( \mathbb{P}^{n}\left( \mathcal{T}\right) \right) $ and \mathbb{S}_{H}^{2n+1}\right) quantum complex spaces $\mathbb{P}^{n}\left( \mathcal{T} spheres $\mathbb{S}_{H}^{2n+1}$, line bundles $L_{k}$ $, studied by Hajac collaborators. Motivated groupoid approach Curto, Muhly, Renault t...

Using a stable equivalence due to Rouquier, we prove that Broué’s abelian defect group conjecture holds for 3-blocks of defect 2 whose Brauer correspondent has a unique isomorphism class of simple modules. The proof makes use of the fact, also due to Rouquier, that a stable equivalence of Morita type between self-injective algebras induces an isomorphism between the connected components of the ...

In this paper we deal with C*-algebras of real rank zero that can be represented as inductive limits A = lim −→(An, νn+1,n) of direct sums of homogeneous C*-algebras of the form An = ⊕ i=1 Pn,iM[n,i](C(Xn,i))Pn,i, where Xn,i are finite CW complexes and Pn,i are selfadjoint projections. Following [3] we called these C*-algebras approximately homogeneous. Our main result asserts that any approxim...

Let A and B be separable C-algebras, B stable. We show that the Connes-Higson construction gives rise to an isomorphism between the group of unitary equivalence classes of extensions of SA by B, modulo the extensions which are asymptotically split, and the homotopy classes of asymptotic homomorphisms from SA to B.