The Kadison-Ringrose cohomology conjecture asserts the vanishing of positive-degree bounded Hochschild cohomology of
a von Neumann algebra with coefficients in
itself. For a complex von Neumann algebra 
,
the degree-
cochains are bounded complex multilinear maps 
. Vanishing means that every bounded cocycle has a
bounded primitive, not merely that it is a limit of coboundaries.
Kadison-Ringrose Cohomology Conjecture
See also
Bounded Hochschild Cohomology, Hochschild-Kamowitz Complex, von Neumann AlgebraExplore with Wolfram|Alpha
References
Sinclair, A. M. and Smith, R. R. "The Hochschild Cohomology Problem for von Neumann Algebras." Proc. Natl. Acad. Sci. USA 95, 3376-3379, 1998. https://doi.org/10.1073/pnas.95.7.3376.Cite this as:
Weisstein, Eric W. "Kadison-Ringrose Cohomology Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Kadison-RingroseCohomologyConjecture.html