Fräissé-Hrushovski predimensions on nilpotent Lie algebras [Elektronische Ressource] / Andrea Amantini. Gutachter: Andreas Baudisch ; Frank O. Wagner ; Enrique Casanovas

Fraïssé-Hrushovski predimensionson nilpotent Lie algebrasDISSERTATIONzur Erlangung des akademischen Gradesdoctor rerum naturaliumim Fach Mathematikeingereicht an derMathematisch-Wissenschaftlichen Fakultät IIHumboldt-Universität zu BerlinvonDipl. Math Andrea AmantiniFlorenz, 28.01.80Präsident der Humboldt-Universität zu Berlin:Prof. Dr. Jan-Hendrik OlbertzDekan der Mathematisch-Wissenschaftlichen Fakultät II:Prof. Dr. Elmar KulkeGutachter:1. Prof. Dr. Andreas Baudisch2. Prof. Dr. Frank O. Wagner3. Prof. Dr. Enrique Casanovaseingereicht am: 08.12.2010Tag der mündlichen Prüfung: 30.05.2011AbstractIn this work, the so called Fraïssé-Hrushowski amalgamation is applied to nilpo-tent graded Lie algebras over the p-elements field with p a prime. We are mainlyconcerned with the uncollapsed version of the original process.The predimension used in the construction is compared with the group theoreticalnotion of deficiency, arising from group Homology.We also describe in detail the Magnus-Lazard correspondence, to switch betweenthe aforementioned Lie algebras and nilpotent groups of prime exponent. In thiscontext, the Baker-Hausdorff formula allows such to be definably interpretedin the corresponding algebras.Starting from the structures which led to Baudisch’ new uncountably categoricalgroup, we obtain anω-stable Lie algebra of nilpotency class 2, as the countable richFraïssé limit of a suitable class of finite algebras overZ .