Subgaussian 1-cocycles on discrete groups

Structural Properties of Inner Amenable Discrete Groups

Shintani Cocycles on GLn

The aim of this paper is to define an n− 1-cocycle σ on GLn(Q) with values in a certain space D of distributions on Af \ {0}. Here Af denotes the ring of finite adèles of Q, and the distributions take values in the Laurent series C((z1, . . . , zn)). This cocycle can be used to evaluate special values of Artin L-functions on number fields at negative integers. The construction generalizes that ...

Differential Calculi over Quantum Groups and Twisted Cyclic Cocycles

We study some aspects of the theory of non-commutative differential calculi over complex algebras, especially over the Hopf algebras associated to compact quantum groups in the sense of S.L. Woronowicz. Our principal emphasis is on the theory of twisted graded traces and their associated twisted cyclic cocycles. One of our principal results is a new method of constructing differential calculi, ...

Integrability of Induction Cocycles for Kac-moody Groups

We prove that whenever a Kac-Moody group over a finite field is a lattice of its buildings, it has a fundamental domain with respect to which the induction cocycle is L for any p∈ [1; +∞). The proof uses elementary counting arguments for root group actions on buildings. The applications are the possibility to apply some lattice superrigidity, and the normal subgroup property for Kac-Moody latti...

TILINGS, FUNDAMENTAL COCYCLES AND FUNDAMENTAL GROUPS OF SYMBOLIC Zd-ACTIONS

We prove that certain topologically mixing two-dimensional shifts of finite type have a ‘fundamental’ 1-cocycle with the property that every continuous 1-cocycle on the shift space with values in a discrete group is continuously cohomologous to a homomorphic image of the fundamental cocycle. These fundamental cocycles are closely connected with representations of the shift space by Wang tilings...