A while ago I heard the following two facts about semi-simple Lie groups (though I have a feeling they may have to be restricted to connected semi-simple Lie groups):(adsbygoogle = window.adsbygoogle || []).push({});

1. That semi-simple Lie groups are classified by their weight (and co-weight) and root (and co-root) lattices;

2. That all of these lattices can be deduced from the fundamental representations of the group. (So that if we have a complete set of representations we can go on and infer the group.)

Can someone confirm for me that these are indeed the case, or suggest a reference where the above are stated? (I am a physics graduate but with little pure math knowledge, so the more approachable the better.) Thanks a lot!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Classification of semi-simple Lie groups

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**