On completion of the course
the student should have the following learning outcomes defined in terms of knowledge, skills and general competence:
Knowledge
The student¿..
- Knows basic homological algebra
- Knows the definitions and basic properties of algebras, co-algebras, bi-algebras, Lie-algebras, DG-algebras, and modules over these.
- Knows Koszul algebras, and Koszul duality.
- Knows the definitions and basic properties algebraic operads and algebras over these. Specifically one knows the operads: Com, Ass, Lie, Poisson, pre-Lie, post-Lie, Leibiniz, Zinbiel, and Diass, and algebras over these.
- Knows basic properties of Hopf-algebras, and examples of such algebras, like the Connes-Kreimer algebra, and other combinatorial Hopf-algebras.
Skills
The student¿..
- Can use algebraic tools which are important for many problems in algebra, topology, and computational mathematics.
- Has solid experience and training in reasoning withabstract mathematical structures
General competence
The student¿..
- Has insight into the development of modern algebraic structures from the last fifty years.
- Has insight into how algebraic structures is a tool to describe structural phenomena in both applied and theoretical mathematics.