Operads are mathematical devices that describe algebraic structures of many varieties and
in various categories. Operads are particularly important in categories with a good notion of …

We develop some of the ingredients needed for string theory on noncommutative
spacetimes, proposing an axiomatic formulation of T-duality as well as establishing a very …

We describe and investigate Arens–Michael envelopes of associative algebras and their
homological properties. We also introduce and study analytic analogs of some classical ring …

We develop the first steps towards an analysis of geometry on the quantum spacetime
proposed in Doplicher et al.(Commun Math Phys 172: 187–220, 1995). The homogeneous …

The central result of this paper is an explicit computation of the Hochschild and cyclic
homologies of a natural smooth subalgebra of stable continuous trace algebras having …

We describe a categorical framework for the classification of D-branes on non-commutative
spaces using techniques from bivariant K-theory of C*-algebras. We present a new …

Let s be the space of rapidly decreasing sequences. We give the spectral representation of
normal elements in the Fr\'echet algebra L (s', s) of the so-called smooth operators. We also …

We prove that the higher harmonic signature of an even dimensional oriented Riemannian
foliation $ F $ of a compact Riemannian manifold $ M $ with coefficients in a leafwise $ U (p …

Automatic continuity and amenability in the non-commutative Schwartz space -
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In this paper we construct a bivariant Chern character defined on “families of spectral
triples”. Such families should be viewed as a version of unbounded Kasparov bimodules …