Root Lattice
The root lattice of En has determinant 9−n, and can be constructed as the lattice of vectors in the unimodular Lorentzian lattice Zn,1 that are orthogonal to the vector (1,1,1,1,....,1|3) of norm n×12 − 32 = n − 9.
Read more about this topic: En (Lie Algebra)
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“I will go root away
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—William Shakespeare (1564–1616)