首页/论文/math/0206252

arXiv math/02062522002-06-24math.OA

Meet Irreducible Ideals and Representations of Limit Algebras

Kenneth R. Davidson, Elias Katsoulis, Justin Peters

备注：: 8 pages; accepted in JFA

英文摘要：

In this paper we give a criterion for an ideal of a TAF algebra to be meet irreducible. We show that an ideal $J$ of $A$ is meet irreducile if and only if the C$^*$-envelope of the quotient $A/J$ is primitive. In that case, A/J admits a nest representation which extends to a *-representation of the C$^*$-envelope for $A/J.$ We also characterize the meet irreducible ideals as the kernels of nest representations; this settles the question of whether the n-primitive and meet irreducible ideals coincide.

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

Meet irreducible ideals in direct limit algebras

We study the meet irreducible ideals in certain direct limit algebras, namely the strongly maximal triangular subalgebras of AF C*-algebras. These ideals have a description in terms of the coordinates, or spectrum, that is a natural extension of one description of meet irreducible ideals in the upper triangular matrices. Additional information is available if the limit algebra is an analytic subalgebra of its C*-envelope or if the analytic algebra is trivially analytic with an injective 0-cocycle. Completely meet irreducible ideals are considered, and a distance formula is presented.

1997-01-21funct-anmath.OA

Inducing Primitive Ideals

We study conditions on a $C^*$-dynamical system $(A,G,α)$ under which induction of primitive ideals (resp. irreducible representations) from stabilizers for the action of $G$ on the primitive ideal space $\Prim(A)$ give primitive ideals (resp. irreducible representations) of the crossed product $A\rtimes_αG$. The results build on earlier results of Sauvageot and others, and will correct a (possibly overly optimistic) statement of the first author.

2006-01-03math.OA

Normed ideal perturbation of irreducible operators in semifinite von Neumann factors

In [10], Halmos proved an interesting result that the set of irreducible operators is dense in $\mathcal B(\mathcal H)$ in the sense of Hilbert-Schmidt approximation. In a von Neumann algebra $\mathcal M$ with separable predual, an operator $a\in \mathcal M$ is said to be {irreducible in} $\mathcal M$ if $W^*(a)$ is an irreducible subfactor of $\mathcal M$, i.e., $W^*(a)'\cap \mathcal M={\mathbb C} \cdot I$. In this paper, let $Φ(\cdot)$ be a $\Vert\cdot\Vert$-dominating, unitarily invariant norm (see Definition 2.1), where by $\Vert\cdot\Vert$ we denote the operator norm. We prove that in eve…

2020-06-21math.OA

The C*-algebra generated by irreducible Toeplitz and composition operators

We describe the C*-algebra generated by an irreducible Toeplitz operator $T_ψ$, with continuous symbol $ψ$ on the unit circle $\mathbb{T}$, and finitely many composition operators on the Hardy space $H^2$ induced by certain linear-fractional self-maps of the unit disc, modulo the ideal of compact operators $K(H^2)$. For composition operators with automorphism symbols, we show that this algebra is not isomorphic to the one generated by the shift and composition operators.

2014-08-05math.OA

不可约映射以及正则开集与正则理想的 Boolean 代数同构

Irreducible Maps and Isomorphisms of Boolean Algebras of Regular Open Sets and Regular Ideals

本文研究紧 Hausdorff 空间间的不可约连续满射，证明正则开集代数与 $C(X)$、$C(Y)$ 中正则理想代数的同构，并刻画紧可度量化空间的 Boolean 等价性。

2023-12-31math.GNmath.OA

Boundary Functions for Ideals in Analytic Limit Algebras

We develop a theory of boundary functions for ideals in trivially analytic subalgebras of simple AF C*-algebras with an injective 0-cocycle, a class which includes all full nest algebras. Boundary functions are maps from the spectrum of the diagonal of the analytic subalgebra to itself. The relation between boundary functions and ideal sets is explored and a description is given of meet and join irreducible boundary functions.

1998-06-08math.OA

更多相关论文收起更多论文

On the ideal structure of the Fourier-Stieltjes algebra of certain groups

We determine the structure of the weak*-closed $G$-invariant ideals in the Fourier-Stieltjes algebra $B(G)$ of certain groups $G$ by means of a $K$-theoretical obstruction. The groups to which this applies are groups whose only irreducible unitary representations that are not weakly contained in the left regular representation are class-one representations. In particular, this is the case for the groups $\mathrm{SL}(2,\mathbb{R})$ and $\mathrm{SL}(2,\mathbb{C})$, which we consider as explicit examples.

2020-05-04math.OA

Ideals of etale groupoid algebras and Exel's Effros-Hahn conjecture

We extend to arbitrary commutative base rings a recent result of Demeneghi that every ideal of an ample groupoid algebra over a field is an intersection of kernels of induced representations from isotropy groups, with a much shorter proof, by using the author's Disintegration Theorem for groupoid representations. We also prove that every primitive ideal is the kernel of an induced representation from an isotropy group; however, we are unable to show, in general, that it is the kernel of an irreducible induced representation. If each isotropy group is finite (e.g., if the groupoid is principal)…

2018-10-30math.OAmath.RA

The topology of ideals in some triangular AF algebras

A set of meet-irreducible ideals is described for a class of maximal triangular almost finite algebras. This set forms a topological space under the hull-kernel closure, and there is a one-to-one correspondence between closed sets in this space and ideals in the AF algebra. Some connections with nest representations and nest-primitive ideals are also described.

1996-01-02funct-anmath.OA

Algebraically irreducible representations and structure space of the Banach algebra associated with a topological dynamical system

If $X$ is a compact Hausdorff space and $σ$ is a homeomorphism of $X$, then a Banach algebra $\ell^1(Σ)$ of crossed product type is naturally associated with this topological dynamical system $Σ=(X,σ)$. If $X$ consists of one point, then $\ell^1(Σ)$ is the group algebra of the integers. We study the algebraically irreducible representations of $\ell^1(Σ)$ on complex vector spaces, its primitive ideals and its structure space. The finite dimensional algebraically irreducible representations are determined up to algebraic equivalence, and a sufficiently rich family of infinite dimensional algebr…

2016-06-14math.FAmath.OA

单边子位移代数的不可约表示

Irreducible representations of one-sided subshift algebras

本文构造了任意字母表上子位移相关有单位代数的表示，用无出口循环描述其忠实性准则，刻画不可约分量等价性，并确定与线路径相关的极小左理想。

2023-06-28math.DSmath.OAmath.RA

Irreducible Representations of Bost-Connes systems

The classification problem of Bost-Connes systems was studied by Cornellissen and Marcolli partially, but still remains unsolved. In this paper, we will give a representation-theoretic approach to this problem. We generalize the result of Laca and Raeburn, which concerns with the primitive ideal space on the Bost-Connes system for $\mathbb{Q}$. As a consequence, the Bost-Connes $C^*$-algebra for a number field $K$ has $h_K^1$-dimensional irreducible representations and does not have finite-dimensional irreducible representations for the other dimensions, where $h_K^1$ is the narrow class numbe…

2015-11-05math.NTmath.OA