We investigate the structures of crossed products of the Cuntz algebra O∞ by quasi-free actions of abelian groups. We completely determine their ideal structures and compute the strong Connes spectra and K-groups.

We establish Sakakibara’s differential equations [Sa04] in a matrix setting for the counter term (respectively renormalized character) in Connes–Kreimer’s Birkhoff decomposition in any connected graded Hopf algebra, thus including Feynman rules in perturbative renormalization as a key example.

We derive simple explicit formulas for the character of a cycle in the Connes’ (b, B)-bicomplex of cyclic cohomology and give applications to the Fredholm modules and equivariant characteristic classes.

We give a universal construction of families of Hopf P-algebras for any Hopf operad P. As a special case, we recover the Connes-Kreimer Hopf algebra of rooted trees.

We relate the author’s Lie cobracket in the module additively generated by loops on a surface with the Connes-Kreimer Lie bracket in the module additively generated by trees.

This is an expository note on non-amenabilty of the Banach algebra B(lp) for p = 1, 2. These were proved respectively by Connes and Read via very different methods. We give a single proof which reproves both.

In this work, the continuously controlled techniques developed by Carlsson and Pedersen are used to prove that the Baum-Connes map is a split injection for groups satisfying certain geometric conditions.

In earlier work the authors introduced dynamic asymptotic dimension, a notion of dimension for topological dynamical systems that applies to many interesting examples. In this paper, we use finiteness of dynamic asymptotic dimension to get information on the K-theory of the associated crossed product C ̊algebras: specifically, we give a new proof of the Baum-Connes conjecture for such actions. T...

We derive simple explicit formula for the character of a cycle in the Connes’ (b, B)-bicomplex of cyclic cohomology and apply it to write formulas for the equivariant Chern character and characters of finitely-summable bounded Fredholm modules.