论文标题
正交统一基础和子因子猜想
Orthogonal Unitary Bases and a Subfactor Conjecture
论文作者
论文摘要
我们表明，任何有限的尺寸von Neumann代数都在其标准轨迹方面承认统一基础。我们还表明，$ M_N（\ Mathbb {C}）$有限的尺寸von Neumann subgra $在归一化矩阵跟踪下允许正常的单一基础，并且仅当且仅当正常化的矩阵跟踪和von Neumann subgebra的标准化矩阵跟踪和标准痕迹时。作为应用程序，我们验证了最近对Bakshi-gupta的猜想，表明任何有限的索引定期包含$ n \ subseteq m $ of $ II_1 $ - fem-factors cumpers cuts cuts cumply pimsner-popa基础。
We show that any finite dimensional von Neumann algebra admits an orthonormal unitary basis with respect to its standard trace. We also show that a finite dimensional von Neumann subalgebra of $M_n(\mathbb{C})$ admits an orthonormal unitary basis under normalized matrix trace if and only if the normalized matrix trace and standard trace of the von Neumann subalgebra coincide. As an application, we verify a recent conjecture of Bakshi-Gupta, showing that any finite-index regular inclusion $N\subseteq M$ of $II_1$-factors admits an orthonormal unitary Pimsner-Popa basis.
