In [Iha86b], Ihara constructs a universal cocycle Gal ( Q/Q ) −→ Zp[[t0, t1, t∞]]/ ((t0 + 1)(t1 + 1)(t∞ + 1)− 1) arising from the action of Gal ( Q/Q ) on certain quotients of the Jacobians of the Fermat curves

Schwinger terms of current algebra can be identiied with nontrivial cyclic cocycles of a Fredholm module. We discuss its temperature dependence. Similar anomalies may occur also in spin systems. In simple examples already an operator{valued cocycle shows up.

Abstract. In this article we prove an existence theorem for solutions of the stochastic Burgers equation (SBE) on the unit interval with Dirichlet boundary conditions and anticipating initial velocities. The SBE is driven by affine (additive + linear) noise. In order to establish the existence theorem, we adopt a somewhat counterintuitive perspective in which stochastic dynamical systems ideas ...

This paper attempts to establish the connection among classifications of gapped boundaries in topological phases of matter, bosonic symmetry-protected topological (SPT) phases and faulttolerantly implementable logical gates in quantum error-correcting codes. We begin by presenting constructions of gapped boundaries for the d-dimensional quantum double model by using d-cocycles functions (d ≥ 2)...

To any cleft Hopf Galois object, i.e., any algebra H obtained from a Hopf algebra H by twisting its multiplication with a two-cocycle α, we attach two “universal algebras” AH and U α H . The algebra A α H is obtained by twisting the multiplication of H with the most general two-cocycle σ formally cohomologous to α. The cocycle σ takes values in the field of rational functions on H. By construct...