Universal deformation rings of modules for algebras of dihedral type of polynomial growth

Let k be an algebraically closed field, and let \Lambda\ be an algebra of dihedral type of polynomial growth as classified by Erdmann and Skowro\'{n}ski. We describe all finitely generated \Lambda-modules V whose stable endomorphism rings are isomorphic to k and determine their universal deformation rings R(\Lambda,V). We prove that only three isomorphism types occur for R(\Lambda,V): k, k[[t]]/(t^2) and k[[t]].Comment: 11 pages, 2 figure

Semi-Classical Theory of Magnetoresistance Anomalies in Ballistic Multi-Probe Conductors

Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe

Integral group ring of Rudvalis simple group

Using the Luthar–Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Rudvalis sporadic simple group Ru. As a consequence, for this group we confirm the Kimmerle conjecture on prime graphs

From shallow to deep divergences:mixed messages from Amazon Basin cichlids

Cichlids are a conspicuous component of Amazonian ichthyofauna, filling a wide range of niches. Yet taxonomy of many groups is still poorly known in the Amazon, and most of the yet-to-be discovered species are concentrated there. We analyzed 230 individuals sampled from six major Amazonian River Basins representing 56 morpho-species, 34 nominal and 22 undescribed species in 18 cichlid genera. We used four different single-locus species-discovery (SLSD) methods, delimiting between 53 (mPTP) and 57 (GMYC) species/lineages. When detected, species/lineages are hierarchically geographically structured. Many groups such as the Geophaginae and the Cichlinae have recently diversified, and species of genera such as Cichla and Symphysodon hybridize or have a history of hybridization; thus, these species will not be detected by SLSD methods. At the same time, for example, the genera Apistogramma and Biotodoma harbor cryptic species. For all these reasons, species/lineage diversity of Amazonian cichlids is significantly underestimated. The diversity of Amazonian cichlids is particularly remarkable given that the 570 species of Neotropical cichlids, many of which are from the Amazon Basin, are found in just 1.7% of the freshwater aquatic habitat in which the ~ 2,000 species of the East African rift lake cichlids evolved.</p