自由量子群的梯度形式与强实性
Gradient forms and strong solidity of free quantum groups
摘要：
考虑自由正交量子群$O_N^+(F)$和自由酉量子群$U_N^+(F)$与$N \geq 3$ .在$F = {\rm id}_N$的情况下，Isono和Fima-Vergnioux证明了相关的有限von Neumann代数$L_\infty(O_N^+)$是强实的。此外，Isono对$L_\infty(U_N^+)$也获得了强的实性.本文证明了一般$F \in GL_N(\mathbb{C})$的von Neumann代数$L_\infty(O_N^+(F))$和$L_\infty(U_N^+(F))$是强实的.在我们的证明的一个关键部分是粗糙的性质的梯度双模与狄利克雷形式的研究，这些代数和建设的导子由于Cipriani-Sauvageot。
英文摘要：
Consider the free orthogonal quantum groups $O_N^+(F)$ and free unitary quantum groups $U_N^+(F)$ with $N \geq 3$. In the case $F = {\rm id}_N$ it was proved both by Isono and Fima-Vergnioux that the associated finite von Neumann algebra $L_\infty(O_N^+)$ is strongly solid. Moreover, Isono obtains strong solidity also for $L_\infty(U_N^+)$ . In this paper we prove for general $F \in GL_N(\mathbb{C})$ that the von Neumann algebras $L_\infty(O_N^+(F))$ and $L_\infty(U_N^+(F))$ are strongly solid. A crucial part in our proof is the study of coarse properties of gradient bimodules associated with Dirichlet forms on these algebras and constructions of derivations due to Cipriani--Sauvageot.
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。
