The embedding theorem for finite depth subfactor planar algebras
The embedding theorem for finite depth subfactor planar algebras
复制标题
有限深度子因子平面代数的嵌入定理
DOI：
10.4171/qt/23
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
David Penneys
中科院分区：
文献类型：
--
作者：
V. Jones;David Penneys
我们从有限冯诺依曼代数的强马尔可夫包含中定义了一个正则相对交换平面代数。对于具有马尔可夫迹的有限维C*-代数的连通单包含，我们证明了该平面代数与包含的Bratteli图的二部图平面代数同构。最后，证明了有限深度子因子平面代数是其主图的二部图平面代数的平面子代数。
We define a canonical relative commutant planar algebra from a strongly Markov inclusion of finite von Neumann algebras. In the case of a connected unital inclusion of finite dimensional C*-algebras with the Markov trace, we show this planar algebra is isomorphic to the bipartite graph planar algebra of the Bratteli diagram of the inclusion. Finally, we show that a finite depth subfactor planar algebra is a planar subalgebra of the bipartite graph planar algebra of its principal graph.