首页/论文/math/0207252

arXiv math/02072522002-07math.OA

A class of C^-algebras generalizing both graph algebras and homeomorphism C^-algebras I, fundamental results

Takeshi Katsura

备注：: 37 pages, some terminologies changed, for example, C^*-correspondences were called Hilbert C^*-bimodules and topological graphs were called continuous graphs

英文摘要：

We introduce a new class of C^*-algebras, which is a generalization of both graph algebras and homeomorphism C^*-algebras. This class is very large and also very tractable. We prove the so-called gauge-invariant uniqueness theorem and the Cuntz-Krieger uniqueness theorem, and compute the K-groups of our algebras.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

A class of C^-algebras generalizing both graph algebras and homeomorphism C^-algebras II, examples

We show that the method to construct C^*-algebras from topological graphs, introduced in our previous paper, generalizes many known constructions. We give many ways to make new topological graphs from old ones, and study the relation of C^*-algebras constructed from them. We also prove that our C^*-algebras have a certain characterization. This gives us another definition of our C^*-algebras.

2005-09-16math.OA

A class of $C^$-algebras generalizing both graph algebras and homeomorphism $C^$-algebras IV, pure infiniteness

This is the final one in the series of papers where we introduce and study the $C^*$-algebras associated with topological graphs. In this paper, we get a sufficient condition on topological graphs so that the associated $C^*$-algebras are simple and purely infinite. Using this result, we give one method to construct all Kirchberg algebras as $C^*$-algebras associated with topological graphs.

2005-09-15math.OA

A class of C^-algebras generalizing both graph algebras and homeomorphism C^-algebras III, ideal structures

We investigate the ideal structures of the C^*-algebras arising from topological graphs. We give the complete description of ideals of such C^*-algebras which are invariant under the so-called gauge action, and give the condition on topological graphs so that all ideals are invariant under the gauge action. We get conditions for our C^*-algebras to be simple, prime or primitive. We completely determine the prime ideals, and show that most of them are primitive. Finally, we construct a discrete graph such that the associated C^*-algebra is prime but not primitive.

2006-03-25math.DSmath.OA

K-theoretic duality for shifts of finite type

C*-algebras generalizing Cuntz-Krieger algebras can be associated to hyperbolic homeomorphisms of compact metric spaces. They satisfy a non-commutative form of Spanier-Whitehead duality with respect to K-theory. We prove this for the case of subshifts of finite type. The special feature of the present situation is that the constructions are all done on the full Fock space and are very explicit, while the general theorem requires much more abstract machinery.

1996-12-31funct-anmath.OA

On some fundamental results about higher-rank graphs and their C*-algebras

Results of Fowler and Sims show that every k-graph is completely determined by its k-coloured skeleton and collection of commuting squares. Here we give an explicit description of the k-graph associated to a given skeleton and collection of squares and show that two k-graphs are isomorphic if and only if there is an isomorphism of their skeletons which preserves commuting squares. We use this to prove directly that each k-graph Λ is isomorphic to the quotient of the path category of its skeleton by the equivalence relation determined by the commuting squares, and show that this extends to a ho…

2011-10-11math.COmath.OA

Existence and examples of quantum isometry group for a class of compact metric spaces

We formulate a definition of isometric action of a compact quantum group (CQG) on a compact metric space, generalizing Banica's definition for finite metric spaces. For metric spaces $(X,d)$ which can be isometrically embedded in some Euclidean space, we prove the existence of a universal object in the category of the compact quantum groups acting isometrically on $(X,d)$. In fact, our existence theorem applies to a larger class, namely for any compact metric space $(X,d)$ which admits a one-to-one continuous map $f : X \raro \IR^n$ for some $n$ such that $d_0(f(x),f(y))=ϕ(d(x,y))$ (where $d_0…

2015-04-22math.MGmath.OAmath.QA

更多相关论文收起更多论文

C*代数的奇异值函数

Singular value functions for C$^*$-algebras

The University of Osaka（大阪大学）

本文引入了C*代数的奇异值函数，推广了紧算子在希尔伯特空间上的奇异值，并讨论了这些奇异值函数的基本性质及若干C*代数类别的示例。

2026-05-17math.FAmath.OA