Search results for " Berezin deformation"

MR3299506 Reviewed Rădulescu, Florin(I-ROME2) On unbounded, non-trivial Hochschild cohomology in finite von Neumann algebras and higher order Berezin…

2015

If (At)t>1 is a family of finite von Neumann algebras with a Chapman-Kolmogorov set of linear maps (symbol system) (Φs,t), and if αt:A→A are isomorphisms in a finite family of von Neumann algebras, the corresponding Hochschild cocycles are related to an obstruction to the deformation of the set of linear maps (Φs,t) in the corresponding Chapman-Kolmogorov system (Φs,t)˜ of completely positive maps. In this set-up, the author introduces an invariant (c,Z) for a finite von Neumann algebra M, consisting of a 2-Hochschild cohomology cocycle c and a coboundary unbounded operator Z for c. With some assumptions on c and Z=α+X+iY (α>0, Y is antisymmetric), the existence of an unbounded derivation δ…