Taking pure mathematics a step further
Pure mathematics, which differs from applied mathematics in that it studies entirely abstract concepts, explores the boundary of mathematics and pure reason. As it requires more creativity and mental capabilities, it can offer new perspectives on many disciplines and help unravel some of our world's mysteries and mechanics. The EU-funded project 'Representation theory of blocks of group algebras with non-abelian defect groups' (B10NONABBLCKSETH) investigated two important areas of pure mathematics related to representation theory of associative algebras and Lie theory. The project studied representations of symmetric groups and specific types of algebras to advance many basic mathematical challenges. In more academic terms, the project team investigated the distinguished class of blocks of symmetric groups with non-abelian defect groups. This included decomposition numbers, Ext-quivers, indecomposable modules, Cartan matrices and properties of gradings related to the relevant algebras. It also mapped connections between different theories and worked on proving various mathematical conjectures that gave rise to more challenges and mathematical problems to study. The project opened the door to several new lines of research that could potentially further what we know about orbits, quivers (types of graphs) and certain advanced geometric models. The research conducted under this project is directly related to Lie groups. These explain continuous symmetry of mathematical objects and structures, representing indispensable tools for many areas of contemporary mathematics and modern theoretical physics. Such research will undoubtedly help advance the field of pure mathematics in Europe and encourage academic debate in the field. It could eventually yield results that may have a positive impact on academia and even on real-life applications, an inherent virtue of any type of mathematics.
