Generalized Cartan matrix

introduction

• Cartan matrix encodes relative lenghths and angles among vectors in the root system.
• symmetrizability condition the generalized Cartan matrix guarantees the existence of invariant bilinar forms

related items

• Rank 2 generalized Cartan matrix

Killing form

• Killing form and invariant symmetric bilinear form

computational resource

• https://docs.google.com/file/d/0B8XXo8Tve1cxdlBHdXA5THp3SFE/edit