The Hochschild cohomology ring of a group algebra is an object that has received recent attention, but is difficult to compute, in even the simplest of cases. In this paper, we use the product formula due to Witherspoon and Siegel to extend some of t
heir computations. In particular, we compute the Hochschild cohomology algebra of group algebras kG where |G| is less than 16, and we provide an alternative computation of the ring $HH^*(k(E ltimes P))$ considered by Kessar and Linckelmann.
Motivated by recent problems regarding the symmetry of Hecke algebras, we investigate the symmetry of the endomorphism algebra $E_P(M)$ for $P$ a $p$-group and $M$ a $kP$-module with $k$ a field of characteristic $p$. We provide a complete analysis f
or cyclic $p$-groups and the dihedral 2-groups. For the dihedral 2-groups, this requires the classification of the indecomposable modules in terms of string modules and band modules. We generalize our techniques to consider $E_{Lambda}(M)$ for $Lambda$ a Nakayama algebra, a local algebra, or even an arbitrary algebra.
(abridged) The technique of gravitational microlensing is currently unique in its ability to provide a sample of terrestrial exoplanets around both Galactic disk and bulge stars, allowing to measure their abundance and determine their distribution wi
th respect to mass and orbital separation. In order to achieve these goals in reasonable time, a well-coordinated effort involving a network of either 2m or 4 x 1m telescopes at each site is required. It could lead to the first detection of an Earth-mass planet outside the Solar system, and even planets less massive than Earth could be discovered. From April 2008, ARTEMiS (Automated Robotic Terrestrial Exoplanet Microlensing Search) is planned to provide a platform for a three-step strategy of survey, follow-up, and anomaly monitoring. As an expert system embedded in eSTAR (e-Science Telescopes for Astronomical Research), ARTEMiS will give advice on the optimal targets to be observed at any given time, and will also alert on deviations from ordinary microlensing light curves by means of the SIGNALMEN anomaly detector. While the use of the VOEvent (Virtual Observatory Event) protocol allows a direct interaction with the telescopes that are part of the HTN (Heterogeneous Telescope Networks) consortium, additional interfaces provide means of communication with all existing microlensing campaigns that rely on human observers. The success of discovering a planet by microlensing critically depends on the availability of a telescope in a suitable location at the right time, which can mean within 10 min. Real-time modelling offers the opportunity of live discovery of extra-solar planets, thereby providing Science live to your home.
