论文标题
中级亚代晶格的晶格
Lattice of intermediate subalgebras
论文作者
论文摘要
Analogous to subfactor theory, employing Watatani's notions of index and $C^*$-basic construction of certain inclusions of $C^*$-algebras, (a) we develop a Fourier theory (consisting of Fourier transforms, rotation maps and shift operators) on the relative commutants of any inclusion of simple unital $C^*$-algebras with finite Watatani index, and (b) we introduce the内部和外部角度的概念中间角度$ c^*$ - 任何包含Unital $ c^*$的子代数 - 代数承认有限指数有条件期望。然后，在[2]的线上，我们应用这些概念以获得任何不可约合包容性的中间$ c^*$ - 子代数的基数，如（a）中的限制，并改善了longo限制的$ iii $ $ iii $因子因子$ iii $ aintex inteex interex Index的中间子因素的基数。此外，我们还表明，对于有限的von Neumann代数，中间von Neumann subergebras的晶格始终是有限的。
Analogous to subfactor theory, employing Watatani's notions of index and $C^*$-basic construction of certain inclusions of $C^*$-algebras, (a) we develop a Fourier theory (consisting of Fourier transforms, rotation maps and shift operators) on the relative commutants of any inclusion of simple unital $C^*$-algebras with finite Watatani index, and (b) we introduce the notions of interior and exterior angles between intermediate $C^*$-subalgebras of any inclusion of unital $C^*$-algebras admitting a finite index conditional expectation. Then, on the lines of [2], we apply these concepts to obtain a bound for the cardinality of the lattice of intermediate $C^*$-subalgebras of any irreducible inclusion as in (a), and improve Longo's bound for the cardinality of intermediate subfactors of an inclusion of type $III$ factors with finite index. Moreover, we also show that for a fairly large class of inclusions of finite von Neumann algebras, the lattice of intermediate von Neumann subalgebras is always finite.
