计算$\mathrm{SU}(2)$上左不变对合结构的上同调空间：例子
Computing cohomology spaces of left-invariant involutive structures on $\mathrm{SU}(2)$: examples
摘要：
本文研究了$\mathrm{SU}(2)$上的左不变对合结构，$\mathrm{SU}(2)$是最简单的非交换紧李群。我们确定了一个单一的复向量场的范围（在光滑拓扑）的封闭性跨越标准CR结构的$\mathrm{SU}(2)$，也计算光滑上同调空间的corank $1$结构。在我们的方法中，最基本的是具体理解环境李群的不可约表示以及左不变向量场如何作用于它们的矩阵系数（我们从Ruzhansky和Turunen（2010）的书中借用）。我们的目的仅仅是提供在以前的论文（2019）中开发的理论的一些简单应用，因为这里显示的结果可能可以通过更直接法获得。
英文摘要：
In these notes we study left-invariant involutive structures on $\mathrm{SU}(2)$, the most naïve non-commutative compact Lie group. We determine closedness of the range (in the smooth topology) of a single complex vector field spanning the standard CR structure of $\mathrm{SU}(2)$ and also compute the smooth cohomology spaces of a corank $1$ structure. In our approach, it is fundamental to understand concretely the irreducible representations of the ambient Lie group and how left-invariant vector fields operate on their matrix coefficients (which we borrow from the book of Ruzhansky and Turunen (2010)). Our purpose is solely to provide some easy applications of the theory developed in a previous paper (2019), as the results shown here can probably be obtained by more direct methods.
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。
