Torsors and ternary Moufang loops arising in projective geometry

We give an interpretation of the construction of torsors from preceding work (Bertram, Kinyon: Associative Geometries. I, J. Lie Theory 20) in terms of classical projective geometry. For the Desarguesian case, this leads to a reformulation of certain results from lot.cit., whereas for the Moufang case the result is new. But even in the Desarguesian case it sheds new light on the relation between the lattice structure and the algebraic structures of a projective space.Comment: 15 p., 5 figure

Associative Geometries. II: Involutions, the classical torsors, and their homotopes

For all classical groups (and for their analogs in infinite dimension or over general base fields or rings) we construct certain contractions, called "homotopes". The construction is geometric, using as ingredient involutions of associative geometries. We prove that, under suitable assumptions, the groups and their homotopes have a canonical semigroup completion.Comment: V2: terminology changed ("torsor" instead of "groud"); some improvements in Chapter 3; to appear in Journal of Lie Theor

Metabolic Engineering of Cyanobacteria for Photosynthetic Production of Drop-In Liquid Fuels

Cyanobacteria are oxygenic phototrophs with great potential as hosts for renewable fuel and chemical production. They grow very quickly (compared with plants) and can use sunlight for energy and CO2 as a carbon source (unlike yeast or E. coli). While cyanobacteria have been engineered to make many chemicals that are native and non-native parts of their metabolism, this work is concerned with the production of heptadecane in Synechocystis sp. PCC 6803. Heptadecane is in a class of natural products produced by all cyanobacteria, but in quantities insufficient for industrialization. Towards this future goal, we have built enabling systems for the overproduction of fuels and chemicals in Synechocystis 6803 and cyanoabacteria generally. These tools include plasmid vectors for the overproduction of heterologous proteins and genome- scale metabolic models that can predict strategies for metabolite overproduction. We have shown that the vectors we developed are helpful in controlling the level and timing of heterologous protein expression using a fluorescent reporter, and have made progress towards heptadecane overproduction. During this process, we have also found that heptadecane is crucial for cold tolerance and modulates cyclic electron flow in photosynthesis. In addition to measuring this phenotype in vivo, we have analyzed it in silico using our genome-scale metabolic model and have gained insight into the role of cyclic electron flow in photosynthesis generally