We study the ideal structure of C∗-algebras arising from C∗-correspondences. We prove that gauge-invariant ideals of our C∗-algebras are parameterized by certain pairs of ideals of original C∗-algebras. We show that our C∗-algebras have a nice property which should be possessed by generalization of crossed products. Applications to crossed products by Hilbert C∗-bimodules and relative Cuntz-Pim...

Secondary homotopy groups supplement the structure of classical homotopy groups. They yield a 2-functor on the groupoid-enriched category of pointed spaces compatible with fiber sequences, suspensions and loop spaces. They also yield algebraic models of (n− 1)-connected (n+1)-types for n ≥ 0. Introduction The computation of homotopy groups of spheres in low degrees in [Tod62] uses heavily secon...

Hyperoctahedral homology for involutive algebras is the theory associated to hyperoctahedral crossed simplicial group. It related equivariant stable homotopy via of infinite loop spaces. In this paper we show that there an E-infinity algebra structure on module computes homology. We deduce admits Dyer-Lashof operations. Furthermore, a Pontryagin product which gives associative, graded-commutati...

A simplicial group is a object in the category of groups. very nice application which polygroup given this paper. Using polygroups instead groups, we already had good results from well known properties due to Loday. Loday proved that crossed module, cat1-group, categories and whose Moore complex length one are equivalent. Loday’s idea present functor groups polygroups. We show there exist cat1-...

We study the Farrell-Jones Conjecture with coefficients in an additive G-category with involution. This is a variant of the L-theoretic FarrellJones Conjecture which originally deals with group rings with the standard involution. We show that this formulation of the conjecture can be applied to crossed product rings R ∗ G equipped with twisted involutions and automatically implies the a priori ...

We study the ideal structure of C∗-algebras arising from C∗-correspondences. We prove that gauge-invariant ideals of our C∗-algebras are parameterized by certain pairs of ideals of original C∗-algebras. We show that our C∗-algebras have a nice property which should be possessed by generalization of crossed products. Applications to crossed products by Hilbert C∗-bimodules and relative Cuntz-Pim...

In this note, we outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed simplicial groups and the homological algebra of module-valued functors. The symmetric homology of group algebras is related to stable homotopy theory. Two sp...

in this paper we study the module contractibility ofbanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. also weinvestigate module contractibility of banach algebras with theconcept of the module diagonal.

Let A be a \C-algebra with an action of finite group G, let $\natural$ 2-cocycle on $G$ and consider the twisted crossed product $A \rtimes \C [G,\natural]$. We determine Hochschild homology [G,\natural]$ for two classes algebras A: - rings regular functions nonsingular affine varieties, graded Hecke algebras. The results are achieved via algebraic families (virtual) representations include des...