Abstract

Let \(A\) and \(B\) be \(C^{*}\)-algebras, and let \(B\) be stable. In this paper, we construct an endofunctor \( \mathfrak R_{X}\) in the category of \(C^{*}\)-algebras for every discrete metric space \(X\) of bounded geometry and introduce the notion of \( \mathfrak R_{X}\)-homotopy of \(*\)-homomorphisms from \(A\) to \( \mathfrak R_{X}B\). We study the existence problem for a group structure on the set of \( \mathfrak R_{X}\)-homotopy classes.

中文翻译：

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一些与 Roe 代数相关的同伦不变函子的可逆性

摘要

令\(A\)和\(B\)为\(C^{*}\) -代数，并令\(B\)稳定。在本文中，我们为有界几何的每个离散度量空间\(X\)构造了一个\(C^{*}\) -代数范畴内的自函子\( \mathfrak R_{X}\)并引入了概念的\( \mathfrak R_{X}\) - 同伦的\(*\) -从\(A\)到\( \mathfrak R_{X}B\) 的同态。我们研究了\( \mathfrak R_{X}\) -同伦类集合上群结构的存在问题。