Objectives and Content
The course gives an introduction to modern algebraic structures developed since the 1960s. These structures are frequently used and studied within algebra, topology and computational mathematics.
The course includes:
¿ Basic homological algebra
¿ Algebras, co-algebras, bi-algebras, Lie algebras and differential graded algebras
¿ Koszul-algebras and Koszul-duality
¿ Algebraic operads and algebras over these
On completion of the course
the student should have the following learning outcomes defined in terms of knowledge, skills and general competence:
- 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.
- 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
- 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.
Required Previous Knowledge
Recommended Previous Knowledge
Compulsory Assignments and AttendanceNo compulsory assignments or attendance
Forms of Assessment
The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.
Type of assessment: Oral examination
- Withdrawal deadline