On fibred biset functors with fibres of order prime and four

This note has two purposes: First, to present a counterexample to a conjecture parametrizing the simple modules over Green biset functors, appearing in an author's previous article. This parametrization fails for the monomial Burnside ring over a cyclic group of order four. Second, to classify the simple modules for the monomial Burnside ring over a group of prime order, for which the above-mentioned parametrization holds

Hochschild cohomology for functors on linear symmetric monoidal categories

Let $R$ be a commutative ring with unit. We develop a Hochschild cohomology theory in the category $\mathcal{F}$ of linear functors defined from an essentially small symmetric monoidal category enriched in $R$-Mod, to $R$-Mod. The category $\mathcal{F}$ is known to be symmetric monoidal too, so one can consider monoids in $\mathcal{F}$ and modules over these monoids, which allows for the possibility of a Hochschild cohomology theory. The emphasis of the article is in considering natural hom constructions appearing in this context. These homs, together with the abelian structure of $\mathcal{F}$ lead to nice definitions and provide effective tools to prove the main properties and results of the classical Hochschild cohomology theory

The (impossible?) formation of acetaldehyde on the grain surfaces: insights from quantum chemical calculations

Complex Organic Molecules (COMs) have been detected in the interstellar medium (ISM). However, it is not clear whether their synthesis occurs on the icy surfaces of interstellar grains or via a series of gas-phase reactions. As a test case of the COMs synthesis in the ISM, we present new quantum chemical calculations on the formation of acetaldehyde (CH3CHO) from the coupling of the HCO and CH3 radicals, both in gas phase and on water ice surfaces. The binding energies of HCO and CH3 on the amorphous water ice were also computed (2333 and 734 K, respectively). Results indicate that, in gas phase, the products could be either CH3CHO, CH4 + CO, or CH3OCH, depending on the relative orientation of the two radicals. However, on the amorphous water ice, only the CH4 + CO product is possible due to the geometrical constraints imposed by the water ice surface. Therefore, acetaldehyde cannot be synthesized by the CH3 + HCO coupling on the icy grains. We discuss the implications of these results and other cases, such as ethylene glycol and dimethyl ether, in which similar situations can occur, suggesting that formation of these molecules on the grain surfaces might be unlikely

Finite metacyclic groups as active sums of cyclic subgroups

The notion of active sum provides an analogue for groups of that of direct sum for abelian groups. One natural question then is which groups are the active sum of cyclic subgroups. Many groups have been found to give a positive answer to this question, while the case of finite metacyclic groups remained unknown. In this note we show that every finite metacyclic group can be recovered as the active sum of a discrete family of cyclic subgroups