A bifinite correspondence between finite von Neumann factors 
and 
is a Hilbert space with commuting
normal unital left 
and right 
actions whose von Neumann module dimensions
are finite on both sides. The actions need not be mutual
commutants. For example, 
with left and right multiplication is an 
-
correspondence of dimension
1 on both sides.
Bifinite Correspondence
See also
Abstract Commensurability, Projective Unitary Representation, Twisted Group von Neumann Algebra, von Neumann Dimension, von Neumann FactorExplore with Wolfram|Alpha
References
Anantharaman, C. and Popa, S. An Introduction to
Factors. https://www.math.ucla.edu/~popa/Books/IIun.pdf.
Cite this as:
Weisstein, Eric W. "Bifinite Correspondence." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BifiniteCorrespondence.html