154,740 research outputs found
Measure continuous derivations on von Neumann algebras and applications to L^2-cohomology
We prove that norm continuous derivations from a von Neumann algebra into the
algebra of operators affiliated with its tensor square are automatically
continuous for both the strong operator topology and the measure topology.
Furthermore, we prove that the first continuous L^2-Betti number scales
quadratically when passing to corner algebras and derive an upper bound given
by Shen's generator invariant. This, in turn, yields vanishing of the first
continuous L^2-Betti number for II_1 factors with property (T), for finitely
generated factors with non-trivial fundamental group and for factors with
property Gamma.Comment: 17 page
Convergence of the Gutt Star Product
In this work we consider the Gutt star product viewed as an associative
deformation of the symmetric algebra S^\bullet(g) over a Lie algebra g and
discuss its continuity properties: we establish a locally convex topology on
S^\bullet(g) such that the Gutt star product becomes continuous. Here we have
to assume a mild technical condition on g: it has to be an Asymptotic Estimate
Lie algebra. This condition is e.g. fulfilled automatically for all
finite-dimensional Lie algebras. The resulting completion of the symmetric
algebra can be described explicitly and yields not only a locally convex
algebra but also the Hopf algebra structure maps inherited from the universal
enveloping algebra are continuous. We show that all Hopf algebra structure maps
depend analytically on the deformation parameter. The construction enjoys good
functorial properties.Comment: 35 pages, minor typos corrected, updated bibliograph
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