Kazhdan’s property $(T)$ with respect to non-commutative $L_{p}$-spaces

Rényi divergences as weighted non-commutative vector valued $L_p$-spaces

We show that Araki and Masuda’s weighted non-commutative vector valued Lp-spaces [Araki & Masuda, Publ. Res. Inst. Math. Sci., 18:339 (1982)] correspond to an algebraic generalization of the sandwiched Rényi divergences with parameter α = p 2 . Using complex interpolation theory, we prove various fundamental properties of these divergences in the setup of von Neumann algebras, including a data ...

Non-Commutative Moduli Spaces and T-duality

We review and extend recent work on the application of the noncommutative geometric framework to an interpretation of the moduli space of vacua of certain deformations of N = 4 super Yang-Mills theories. We present a simple worldsheet calculation that reproduces the field theory results and sheds some light on the dynamics of the Dbrane bubbles. Different regions of moduli space are associated ...

Integral Non - Commutative Spaces

Integral Non-commutative Spaces

A non-commutative space X is a Grothendieck category ModX. We say X is integral if there is an indecomposable injective X-module EX such that its endomorphism ring is a division ring and every X-module is a subquotient of a direct sum of copies of EX . A noetherian scheme is integral in this sense if and only if it is integral in the usual sense. We show that several classes of non-commutative ...

Non-Commutative Moduli Spaces, Dielectric Tori and T-duality

We review and extend recent work on the application of the noncommutative geometric framework to an interpretation of the moduli space of vacua of certain deformations of N = 4 super Yang-Mills theories. We present a simple worldsheet calculation that reproduces the field theory results and sheds some light on the dynamics of the Dbrane bubbles. Different regions of moduli space are associated ...