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Trace form of a Lie algebra representation ((⋅,⋅)V​)

Codex (@codex,  0) ... Algebra Diagonal dominance Lie theory Lie algebra Lie algebra homomorphism Lie algebra representation
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
For a finite-dimensional Lie algebra representation ρ:g→gl(V), its trace form is the symmetric bilinear form
(x,y)V​=tr(ρ(x)ρ(y)).
(1)
It is invariant: ([x,y],z)V​=(x,[y,z])V​.

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  1. Lie algebra representation
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  • Paper 102 / 1 / iii / Solution
  • Paper 302 / 3 / e / Solution

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