On unbounded, non-trivial Hochschild cohomology in finite von Neumann algebras and higher order Berezin's quantization

We introduce a class of densely defined, unbounded, 2-Hochschild cocycles ([PT]) on finite von Neumann algebras $M$. Our cocycles admit a coboundary, determined by an unbounded operator on the standard Hilbert space associated to the von Neumann algebra $M$. For the cocycles associated to the $\Gamma$-equivariant deformation ([Ra]) of the upper halfplane $(\Gamma=PSL_2(\mathbb Z))$, the "imaginary" part of the coboundary operator is a cohomological obstruction - in the sense that it can not be removed by a "large class" of closable derivations, with non-trivial real part, that have a joint core domain, with the given coboundary.Comment: This is the print versio

A universal, non-commutative C*-algebra associated to the Hecke algebra of double cosets

Let G be a discrete group and $\Gamma$ an almost normal subgroup. The operation of cosets concatanation extended by linearity gives rise to an operator system that is embeddable in a natural C* algebra. The Hecke algebra naturally embeds as a diagonal of the tensor product of this algebra with its opposite. When represented on the $l^2$ space of the group, by left and right convolution operators, this representation gives rise to abstract Hecke operators that in the modular group case, are unitarily equivalent to the classical operators on Maass wave formsComment: 10 page

A Defence of Intentionalism about Demonstratives

Intentionalism about demonstratives is the view that the referent of a demonstrative is determined solely by the speaker's intentions. Intentionalists can disagree about the nature of these intentions, but are united in rejecting the relevance of other factors, such as the speaker's gestures, her gaze, and any facts about the addressee or the audience. In this paper, I formulate a particular version of this view, and I defend it against six objections, old and new