Lie algebras MOC

Generalized Cartan matrix

A generalized Cartan matrix is an matrix such that for all lie

2. if ;
3. iff .

The quiver associated to has vertices and edges between vertices and , thus its adjacency matrix . A quiver which can be associated to a generalized Cartan matrix is called a Cartan quiver, hence a Cartan quiver is a quiver with

• no loops
• every edge having at least one edge in the opposite direction

Properties

• In the context of the Mutation and numbers games, transitions between populations and weights on an associated quiver.

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