关于Frobenius自同态的迹

Twisted Burnside-Frobenius theory for endomorphisms of polycyclic groups

Let $R(ϕ)$ be the number of $ϕ$-conjugacy (or Reidemeister) classes of an endomorphism $ϕ$ of a group $G$. We prove for several classes of groups (including polycyclic) that the number $R(ϕ)$ is equal to the number of fixed points of the induced map of an appropriate subspace of the unitary dual space $\widehat G$, when $R(ϕ)<\infty$. Applying the result to iterations of $ϕ$ we obtain Gauss congruences for Reidemeister numbers. In contrast with the case of automorphisms, studied previously, we have a plenty of examples having the above finiteness condition, even among groups with $R_\infty$ pr…

稳定连续迹C^*-代数的自同态

Endomorphisms of Stable Continuous-Trace C^*-algebras

利用谱上有限维向量丛中的满射乘法不变量，对稳定连续迹C^*-代数的保谱自同态进行了分类，直到内自同构.专门的自同构，这给了一个不同的方法的结果菲利普斯和雷伯恩。

II_1因子的若干自同态：部分II

Some endomorphisms of II_1 factors: part II

对任意有限维C^*-代数A，其迹向量\vec s为有理数，我们给出了超有限II_1因子R的一个自同态Φ使得：对所有k个\in \mathbb {N}，Φ^k（R）' \cap R= \otimes^k A. R上的标准迹τ是A上的迹向量\vec s的延拓。因此，最小投影不一定彼此相等。

超有限$II_1$因子的若干自同态

Some endomorphisms of the hyperfinite $II_1$ factor

对任意有限维C*-代数A，其迹向量{ \vec s}的分量为有理数，我们给出了超有限II_1因子R的一个自同态Φ使得：对{ \mathbb N} Φ^k（R）'中的所有k，\cap R= \otimes^k A R上的标准迹τ扩张了A上的迹向量{ \vec s}.作为推论，我们构造了一类超有限II_1因子N^λ \subset M^λ的单参数包含族，其中平凡相对交换子（N^λ）' \cap M^λ= { \mathbb C}和Jones指标[M^λ：N^λ]= λ^{-1} \in（四、\infty）\cap { \mathbb Q}这部分地解决了在超有限II_1因子中求具有平凡相对交换子的子因子的指数的所有可能值的问题，通过证明任何有理数λ^{-1} > 4都可能发生。

On Bounded Finite Potent Operators on arbitrary Hilbert Spaces

The aim of this work is to study the structure of bounded finite potent endomorphisms on Hilbert spaces. In particular, for these operators, an answer to the Invariant Subspace Problem is given and the main properties of its adjoint operator are offered. Moreover, for every bounded finite potent endomorphism we show that Tate's trace coincides with the Leray trace and with the trace defined by R. Elliott for Riesz Trace Class operators.

C ~*-代数的莱夫谢茨数

Lefschetz numbers for C*-algebras

利用Poincare对偶，给出了一个计算满足Poincare对偶和Kunneth定理的可分核C*-代数的自同态的莱夫谢茨数的Lefschetz型公式. (The自同态的莱夫谢茨数是K-理论上的诱导映射在复数张量下的分次迹，与经典情形一样。）然后考虑Cuntz-Krieger代数O_A的自同态。自同态有一个不变量，它是无限集的置换，该置换的收缩和扩张行为描述了自同态的莱夫谢茨数。利用这种描述，我们得到了一个封闭的多项式公式的莱夫谢茨数取决于矩阵A和自同态的介绍。