Introduction to Cluster Algebras and Their Types - Lecture 2

Delve into the world of cluster algebras in this comprehensive lecture by Jacob Matherne at the International Centre for Theoretical Sciences. Explore finite type cluster algebras, valued quivers, and reflection groups. Learn about root systems, simple systems, and crystallographic root systems. Discover the intricacies of Dynkin diagrams and their significance in cluster algebra theory. Examine important theorems by Cartan-Killing and Fomin-Zelevinsky. Gain insights into the connections between cluster algebras and various mathematical fields, including string theory, Poisson geometry, and representation theory. Engage with complex concepts through examples and a Q&A session, making this lecture suitable for graduate students, researchers, and mathematicians interested in expanding their knowledge of cluster algebras and their applications.

Introduction to cluster algebras and their types Lecture 2
Finite type cluster algebra
Valued quiver
Reflection groups
Definition of reflection
Definition of reflection group
Example 1
Root systems
Example 2
Simple systems
Crystallographic root systems and Dynkin diagrams
Definition of the Dynkin diagram
Theorem Cartan - Killing
Theorem Fomin - Zekvinsky '03 CA2
Q&A