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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
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