On Automorphisms and Focal Subgroups of Blocks

Given a p-block B of a finite group with defect group P and fusion system on P, we show that the rank of the group is invariant under stable equivalences of Morita type. The main ingredients are the construction, due to Broué and Puig, a theorem of Weiss on linear source modules, arguments of Hertweck and Kimmerle applying Weiss’ theorem to blocks, and connections with integrable derivations in the Hochschild cohomology of block algebras

Unusual magneto-transport of YBa2Cu3O7-d films due to the interplay of anisotropy, random disorder and nanoscale periodic pinning

We study the general problem of a manifold of interacting elastic lines whose spatial correlations are strongly affected by the competition between random and ordered pinning. This is done through magneto-transport experiments with YBa2Cu3O7-d thin films that contain a periodic vortex pinning array created via masked ion irradiation, in addition to the native random pinning. The strong field-matching effects we observe suggest the prevalence of periodic pinning, and indicate that at the matching field each vortex line is bound to an artificial pinning site. However, the vortex-glass transition dimensionality, quasi-2D instead of the usual 3D, evidences reduced vortex-glass correlations along the vortex line. This is also supported by an unusual angular dependence of the magneto-resistance, which greatly differs from that of Bose-glass systems. A quantitative analysis of the angular magnetoresistance allows us to link this behaviour to the enhancement of the system anisotropy, a collateral effect of the ion irradiation