论文标题
来自Cuntz代数的Higman-Thompson组的代表
Representations of Higman-Thompson groups from Cuntz algebras
论文作者
论文摘要
Cuntz Algebra $ \ Mathcal {O} _n $的每个表示都会导致Higman-Thompson Group $ v_n $的单一表示。我们考虑家庭$ \ {π_x\} _ {x \ in [0,1 [} $的$ \ Mathcal {o} _n $的定位表示$，它们是从间隔映射$ f（x）= x）= nx $（mod 1）在每个典型的典型范围内的元素和一个单位equival equivalsive andirecrience andire andirecival andirecrience andirecrience andirecrience andirecival和nir equivalsive andirecivalsive和Irred equivalsival andirecivalsival的nx $（mod 1）产生的。 $ \ {ρ_x\} _ {x \ in [0,1 [} $ higman-thompson $ v_n $的表示形式，表明这些表示的确是不可修复的，而且仅在$ x $ y $ x $ y $ y $ y $ y $ y $ x $ y y时，这些表示的$ρ_x$和$ρ_x$和$ρ_y$是同等的。
Every representation of the Cuntz algebra $\mathcal{O}_n$ leads to a unitary representation of the Higman-Thompson group $V_n$. We consider the family $\{π_x\}_{x\in [0,1[}$ of permutative representations of $\mathcal{O}_n$ that arise from the interval map $f(x)=nx$ (mod 1) acting on the Hilbert space that underlies each orbit, and then study the unitary equivalence and the irreducibility of the corresponding family $\{ρ_x\}_{x\in [0,1[}$ of representations of Higman-Thompson group $V_n$, showing that that these representations are indeed irreducible and moreover $ρ_x$ and $ρ_y$ are equivalent if and only if the orbits of $x$ and $y$ coincide.
