Von Neumann Algebras
Depth, in the context of subfactor lattices, refers to a measure of the complexity of a subfactor, which is a specific type of inclusion between von Neumann algebras. It captures how 'deep' or 'nested' the connections are within the structure of the subfactor, typically measured by the number of layers or steps needed to reach from one algebra to another through intermediate algebras. This concept is essential for understanding the classification and properties of these algebras as they relate to operator algebras and their representations.
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