Descent of Equivalences and Character Bijections

Categorical equivalences between block algebras of finite groups—such as Morita and derived equivalences—are well known to induce character bijections which commute with the Galois groups of field extensions. This is the motivation for attempting to realise known Morita and derived equivalences over non-splitting fields. This article presents various results on the theme of descent to appropriate subfields and subrings. We start with the observation that perfect isometries induced by a virtual Morita equivalence induce isomorphisms of centres in non-split situations and explain connections with Navarro’s generalisation of the Alperin–McKay conjecture. We show that Rouquier’s splendid Rickard complex for blocks with cyclic defect groups descends to the non-split case. We also prove a descent theorem for Morita equivalences with endopermutation source

Oligomeric Coiled-Coil Adhesin YadA Is a Double-Edged Sword

Yersinia adhesin A (YadA) is an essential virulence factor for the food-borne pathogens Yersinia enterocolitica and Yersinia pseudotuberculosis. Suprisingly, it is a pseudogene in Yersinia pestis. Even more intriguing, the introduction of a functional yadA gene in Y. pestis EV76 was shown to correlate with a decrease in virulence in a mouse model. Here, we report that wild type (wt) Y. enterocolitica E40, as well as YadA-deprived E40 induced the synthesis of neutrophil extracellular traps (NETs) upon contact with neutrophils, but only YadA-expressing Y. enterocolitica adhered to NETs and were killed. As binding seemed to be a prerequisite for killing, we searched for YadA-binding substrates and detected the presence of collagen within NETs. E40 bacteria expressing V98D,N99A mutant YadA with a severely reduced ability to bind collagen were found to be more resistant to killing, suggesting that collagen binding contributes significantly to sensitivity to NETs. Wt Y. pestis EV76 were resistant to killing by NETs, while recombinant EV76 expressing YadA from either Y. pseudotuberculosis or Y. enterocolitica were sensitive to killing by NETs, outlining the importance of YadA for susceptibility to NET-dependent killing. Recombinant EV76 endowed with YadA from Y. enterocolitica were also less virulent for the mouse than wt EV76, as shown before. In addition, EV76 carrying wt YadA were less virulent for the mouse than EV76 expressing YadAV98D,N99A. The observation that YadA makes Yersinia sensitive to NETs provides an explanation as for why evolution selected for the inactivation of yadA in the flea-borne Y. pestis and clarifies an old enigma. Since YadA imposes the same cost to the food-borne Yersinia but was nevertheless conserved by evolution, this observation also illustrates the duality of some virulence functions