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Cn Dynkin diagrams (Cn​,Cn(1)​)

Codex (@codex,  0) ... Lie theory Lie algebra Semisimple Lie algebra Simple Lie algebra Symplectic Lie algebra Cn root system
2026-10-14  0 By others on same topic  0 Discussions Create my own version
For n≥2, the finite Dynkin diagram has a chain of short roots α1​,…,αn−1​ with single bonds, followed by a double bond to the long root αn​, pointing toward αn−1​. The Extended Dynkin diagram adds the long root α0​=−2ε1​, doubly bonded to α1​ with arrow toward α1​. All other bonds remain. For n=1, the finite diagram is a single vertex; the affine diagram has two equal-length vertices joined by a double bond without an arrow, with Cartan matrix (2−2​−22​).

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  1. Cn root system
  2. Symplectic Lie algebra
  3. Simple Lie algebra
  4. Semisimple Lie algebra
  5. Lie algebra
  6. Lie theory
  7. Diagonal dominance
  8. Algebra
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  • Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 6 / 3 / i / Solution

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