Fourier Invariant Partially approximating subalgebras of the irrational rotation C*-algebra

Morita equivalent subalgebras of irrational rotation algebras and real quadratic fields

In this paper, we determine the isomorphic classes of Morita equivalent subalgebras of irrational rotation algebras. It is based on the solution of the quadratic Diophantine equations. We determine the irrational rotation algebras that have locally trivial inclusions. We compute the index of the locally trivial inclusions of irrational rotation algebras.

A Non-Spectral Dense Banach Subalgebra of the Irrational Rotation Algebra

We give an example of a dense, simple, unital Banach subalgebra $A$ of the irrational rotation C*-algebra $B$, such that $A$ is not a spectral subalgebra of $B$. This answers a question posed in T.W. Palmer's paper [1].

Frobenius-Rieffel norms on finite-dimensional C*-algebras

In 2014, Rieffel introduced norms on certain unital C*-algebras built from conditional expectations onto unital C*-subalgebras. We begin by showing that these norms generalize the Frobenius norm, and we provide explicit formulas for certain conditional expectations onto unital C*-subalgebras of finite-dimensional C*-algebras. This allows us compare these norms to the operator norm by finding explicit equivalence constants. In particular, we find equivalence constants for the standard finite-dimensional C*-subalgebras of the Effros-Shen algebras that vary continuously with respect to their give…

Isomorphism of uniform algebras on the 2-torus

For $α$ a positive irrational, let $\mathcal{A}_α$ be the subalgebra of continuous functions on the two-torus whose Fourier transform vanishes at $(m, n)$ if $m + αn < 0.$ These algebras were studied by Wermer and others, who proved properties such as maximality and characterized the Gelfand space. One of the major themes of current work in operator algebras is classification, but none of the properties which were investigated earlier distinguished between $\mathcal{A}_α$ and $\mathcal{A}_β,$ if $β$ is another positive irrational. We address this question. We also determine the automorphism gr…

On generalized universal irrational rotation algebras and the operator $u+v$

We introduce a class of generalized universal irrational rotation $C^*$-algebras $A_{θ,γ}=C^*(x,w)$ which is characterized by the relations $w^*w=ww^*=1$, $x^*x=γ(w)$, $xx^*=γ(e^{-2πiθ}w)$, and $xw=e^{-2πiθ}wx$, where $θ$ is an irrational number and $γ(z)\in C(\mathbb{T})$ is a positive function. We characterize tracial linear functionals, simplicity, and $K$-groups of $A_{θ,γ}$ in terms of zero points of $γ(z)$. We show that if $A_{θ,γ}$ is simple then $A_{θ,γ}$ is an $A{\mathbb T}$-algebra of real rank zero. We classify $A_{θ,γ}$ in terms of $θ$ and zero points of $γ(z)$. Let $A_θ=C^*(u,v)$ …

$\boldsymbol{\rm \text{非阿贝尔因子：}}$$\boldsymbol{\rm \text{Z}}$$\boldsymbol{\rm \text{群作用与其他非}}$$\boldsymbol{\rm C^*}$$\boldsymbol{\rm \text{-单群的作用}}$$\boldsymbol{\rm \text{（注：原标题为 Non-Abelian Factors for Actions of } \rm \text{Z} \text{ and Other Non-} C^*\text{-Simple Groups，保留符号）}}$

Non-Abelian Factors for Actions of $\mathbb{Z}$ and Other Non-$C^*$-Simple Groups

本研究针对可数群的紧致拓扑动力系统，探讨非交叉积形式的中间$C^*$-子代数的存在性，证明非$C^*$-单群带不变测度时必存在此类子代数，并完整刻画整数群无理旋转系统中的所有这类子代数。