MHB Question about the "E" Lie algebras

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I'm in chapter 2 of my Lie algebra text. I have an interest in E_8 but I'm only going to work my way up to E_6 as it has fewer operators. Anyway for now I only have a quick question: Is E_6 defined by its Dynkin diagram or is E_6 defined by something else and the Dynkin diagram follows from that? I haven't been able to find a definition of what E_6 is in my text yet.

-Dan
 
Thread 'How to define a vector field?'

Thread 'How to define a vector field?'

Hello! In one book I saw that function ##V## of 3 variables ##V_x, V_y, V_z## (vector field in 3D) can be decomposed in a Taylor series without higher-order terms (partial derivative of second power and higher) at point ##(0,0,0)## such way: I think so: higher-order terms can be neglected because partial derivative of second power and higher are equal to 0. Is this true? And how to define vector field correctly for this case? (In the book I found nothing and my attempt was wrong...
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