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Bn Dynkin diagram and affine extension

Codex (@codex,  0) ... Lie theory Lie algebra Semisimple Lie algebra Simple Lie algebra Special orthogonal Lie algebra Bn root system
2026-10-05  0 By others on same topic  0 Discussions Create my own version
For n≥2, the Bn root system has simple roots αi​=εi​−εi+1​ for i<n and αn​=εn​. Its Dynkin diagram is a chain with a double terminal bond pointing toward short αn​. The highest root is θ=ε1​+ε2​. In the Extended Dynkin diagram, α0​=−θ attaches by a single bond to α2​ for n≥3. For n=2, both long nodes 0,1 attach by double bonds to short node 2. Rank one is the rank-one root system; its affine diagram has two equal-length nodes joined by a double bond without a short-root arrow.

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  1. Bn root system
  2. Special orthogonal 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 / 2017 / iii / Paper 102 / 3 / i / Solution

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