# ALGB: Algebra, Incidence Geometry

### About ALGB

The research unit ALGB (Algebra) investigates fundamental structural problems of several algebraic and geometric objects. The motivation mainly comes from those objects and theories that are of importance and interest in several fundamental areas of mathematics, such as number theory, representation theory of algebras and groups, quantum group and Hopf algebra theory, ring theory, group and semigroup theory, algebraic geometry and category theory. On one hand, investigations are done on open classical problems concerning classical algebraic constructions (such as group rings, polynomial rings and their generalizations), and on the other hand, because of the booming interest and need for new algebraic and geometric methods, investigations are being done in rapidly developing areas, such as for example non-commutative geometry and quantum groups and their representations.

So, the scope of the research has many connections with different central topics in mathematics. We list the main areas in which actively ongoing research is being done. Also the members presently involved are listed.

- Incidence Geometry: Ph. Cara, J. De Beule
- Permutation Groups: Ph. Cara
- Group Rings and Unit groups of orders: E. Jespers
- Ring Theory: E. Jespers
- Group and Semigroup Theory: E. Jespers,
- Non-Commutative Geometry: M. Van den Bergh
- Hopf algebras and quantum groups: S. Caenepeel