关于循环幂的一个注记

A Note on the Free and Cyclic Differential Calculus

In 2000, Voiculescu proved an algebraic characterization of cyclic gradients of noncommutative polynomials. We extend this remarkable result in two different directions: first, we obtain an analogous characterization of free gradients; second, we lift both of these results to Voiculescu's fundamental framework of multivariable generalized difference quotient rings. For that purpose, we develop the concept of divergence operators, for both free and cyclic gradients, and study the associated (weak) grading and cyclic symmetrization operators, respectively. One the one hand, this puts a new compl…

关于自由无散度向量场的注记

A note on free divergence-free vector fields

本文展示了全Fock空间上循环梯度与齐次自由无散度向量场的基，确定了Voiculescu自由无散度向量场的维数，并给出了相关正交投影的具体公式。

循环群作用在环上的同伦公式

Homotopy formulas for cyclic groups acting on rings

当环有范数为1的元素时，作用在环上的有限群的正上同调群为零。当群是循环群时，我们给出了上链水平上的显同伦，这使得我们可以将循环群的任何上循环表示为显上链的上边界。本说明中的公式与以前与Eli Aljadeff联合工作中考虑的有效问题密切相关。

Nesbitt and Shapiro Cyclic Sum Inequalities for Positive Definite Matrices

The aim of this note is to show that certain number theoretic inequalities due to Nesbitt and Shapiro have noncommutative counterparts involving positive definite matrices.

系数为循环商奇点的代数K理论

Algebraic K-theory with coefficients of cyclic quotient singularities

本文将Amiot-Iyama-Reiten和Thanhoffer de Volcsey-Van den Bergh关于Cohen-Macaulay模的工作与作者以前关于轨道范畴的工作相结合，计算了具有循环商奇点系数的（非连通）代数K理论.

关于超矩阵的循环同调

On the cyclic homology of supermatrices

本文的目的是证明作者在另一篇文章中构造的广义超迹，它诱导了超代数的Hochschild同调与$A$上给定类型的超方阵超代数的Hochschild同调之间的同构，也诱导了这两个超代数的循环同调之间的同构.