On Picard groups of blocks of finite groups

We show that the subgroup of the Picard group of ap-block ofa finite group given by bimodules with endopermutation sources modulo theautomorphism group of a source algebra is determined locally in terms of thefusion system on a defect group. We show that the Picard group of a block overa complete discrete valuation ringOof characteristic zero with an algebraicclosurekofFpas residue field is a colimit of finite Picard groups of blocks overp-adic subrings ofO. We apply the results to blocks with an abelian defectgroup and Frobenius inertial quotient, and specialise this further to blockswith cyclic or Klein four defect groups

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

The structure of blocks with a Klein four defect group

We prove Erdmann’s conjecture [16] stating that every block with a Klein four defect group has a simple module with trivial source, and deduce from this that Puig’s finiteness conjecture holds for source algebras of blocks with a Klein four defect group. The proof uses the classification of finite simple groups

Stabilization of glucosyl dioxolenium Ions by "dual participation" of the 2,2-dimethyl-2-(ortho-nitrophenyl)acetyl (DMNPA) protection group for 1,2-cis-glucosylation

The stereoselective introduction of glycosidic bonds is of paramount importance to oligosaccharide synthesis. Among the various chemical strategies to steer stereoselectivity, participation by either neighboring or distal acyl groups is used particularly often. Recently, the use of the 2,2-dimethyl-2-(ortho-nitrophenyl)acetyl (DMNPA) protection group was shown to offer enhanced stereoselective steering compared to other acyl groups. Here, we investigate the origin of the stereoselectivity induced by the DMNPA group through systematic glycosylation reactions and infrared ion spectroscopy (IRIS) combined with techniques such as isotopic labeling of the anomeric center and isomer population analysis. Our study indicates that the origin of the DMNPA stereoselectivity does not lie in the direct participation of the nitro moiety but in the formation of a dioxolenium ion that is strongly stabilized by the nitro group.NWONWO-VICI grant VI.C.182.020Bio-organic Synthesi

Cellular Fucosylation Inhibitors Based on Fluorinated Fucose-1-phosphates**

Contains fulltext : 230710.pdf (Publisher’s version ) (Open Access)19 februari 202