论文标题
单型自由正交量子组强的1界
Strong 1-Boundedness of Unimodular Free Orthogonal Quantum Groups
论文作者
论文摘要
最近，Brannan和Vergnioux表明，免费的正交量子组因子$ \ MATHCAL {l} \ MATHBB {F} O_M $具有Jung的强大1-构建属性，因此并不是免费组因子的同构。我们证明了另一个单模型的情况是一个类似的结果，其中参数矩阵是2N尺寸中的标准符号矩阵$ J_ {2N} $。我们通过通过Pauli矩阵的基本表示来介绍自我伴侣发生器来计算定义关系的自由衍生物，从而导致这些发生器的1个结合性。此外，我们证明，在某些条件下，可以将元素添加到1结合的集合而不会失去1局部。特别是这使我们能够包括基本表示的特征，证明了强大的1束缚。
Recently, Brannan and Vergnioux showed that the free orthogonal quantum group factors $\mathcal{L}\mathbb{F}O_M$ have Jung's strong 1-boundedness property, and hence are not isomorphic to free group factors. We prove an analogous result for the other unimodular case, where the parameter matrix is the standard symplectic matrix in 2N dimensions $J_{2N}$. We compute free derivatives of the defining relations by introducing self-adjoint generators through a decomposition of the fundamental representation in terms of Pauli matrices, resulting in 1-boundedness of these generators. Moreover, we prove that under certain conditions, one can add elements to a 1-bounded set without losing 1-boundedness. In particular this allows us to include the character of the fundamental representation, proving strong 1-boundedness.
