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Project

Developments and applications of categorical algebra (FWOTM933)

With the introduction of semi-abelian categories, several new methods and strategies in the context of categorical algebra have been discovered that help obtain new applications.
The objective of this proposal is twofold: to use computational and algebraic methods in order to advance in the development of categorical algebra, and to apply the existing categorical-algebraic knowledge and techniques in order to obtain novel approaches of problems in diverse fields of mathematics.
In particular, we plan to use computational algebra and the open-source package SINGULAR to find a purely categorical characterisation of the variety of groups, result that will help us establish an algebraic correspondence between groups and Lie algebras. Note that currently only the classic geometric approach is available.
In parallel, we plan to develop a new approach to the Cartier-Kostant-Milnor-Moore theorem for cocommutative Hopf algebras,
with the aim of extending it to all fields of zero characteristic. This crucially depends on the host group's knowledge in descent theory and Hopf theory.
This FWO fellowship will combine the categorical and computational skill-set of the candidate together with the experience and training capacities of the host group, initiating and sustaining an interaction between two distinct fields, joining two networks for collaboration in fundamental research, and enriching the candidate's career in his goal of establishing himself as a mature independent researcher.
Date:1 Oct 2018  →  Today
Keywords:algebra
Disciplines:General mathematics