Computing with matrix groups and Lie algebras: new concepts and applications

Computational algebra combines symbolic computation and pure research in algebra, and is concerned with the design of algorithms for solving mathematical problems endowed with algebraic structure. Matrix groups and Lie algebras are prominent algebraic objects describing the natural concept of symmetry. Their importance and omnipresence in science is in contrast to the paucity of algorithms to study their structure. This project will develop deep new mathematical theories for computing with these objects, leading to groundbreaking advances in computational algebra, and providing powerful tools facilitating new research, also in other sciences. The new functionality will be used to solve two classification problems in group and Lie theory.