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Homotopy classification of Leavitt path algebras
(Academic Press Inc Elsevier Science, 2020-03)
In this paper we address the classification problem for purely infinite simple Leavitt path algebras of finite graphs over a field ℓ. Each graph E has associated a Leavitt path ℓ-algebra L(E). There is an open question ...
Cyclic homology, tight crossed products, and small stabilizations
(European Mathematical Society, 2014-12)
In [1] we associated an algebra 1.A/ to every bornological algebra A and an ideal IS.A/ C 1.A/ to every symmetric ideal S C `1. We showed that IS.A/ has K-theoretical properties which are similar to those of the usual ...
Algebraic bivariant K-theory and Leavitt path algebras
(European Mathematical Society, 2021-02-02)
We investigate to what extent homotopy invariant, excisive and matrix stable homology theories help one distinguish between the Leavitt path algebras L.E/ and L.F / of graphs E and F over a commutative ground ring `. We ...
The homotopy types of the posets of p-subgroups of a finite group
(Academic Press Inc Elsevier Science, 2018-04)
We study the homotopy properties of the posets of p-subgroups Sp(G) and Ap(G) of a finite group G, viewed as finite topological spaces. We answer a question raised by R.E. Stong in 1984 about the relationship between the ...
C*- Modular Vector States
(Birkhauser Verlag Ag, 2005-06)
Let B be a C^*-algebra and X a Hilbert C^*B-module. If p ∈ B is a projection, let S_p (X) = {x∈ X : (x,x) =p} be the p-sphere of X. For φ a state of B with support p in B and x ∈ S_p(X), consider the modular vector state ...
States with equivalent supports
(Theta Foundation, 2005-12)
Let B be a von Neumann algebra and X a C* Hilbert B-module. If p ∈ B is a projection, denote by S_p(X) ={x ∈ X(x,x) =p}, the p-sphere of X. For φ a state of B with support p ∈ B and x ∈ S_p(X), consider the state φ_x of ...
Projective space of a C*-module
(World Scientific, 2011-11)
Let X be a right Hilbert C^*-module over A. We study the geometry and the topology of the projective space P(X) of X, consisting of the orthocomplemented submodules of X which are generated by a single element. We also ...
A stronger reformulation of Webb's conjecture in terms of finite topological spaces
(Academic Press Inc Elsevier Science, 2019-06)
We investigate a stronger formulation of Webb's conjecture on the contractibility of the orbit space of the p-subgroup complexes in terms of finite topological spaces. The original conjecture, which was first proved by ...