Last Updated
：2025/12/08
Capelli's identity
Proper noun
Japanese Meaning
数学における公式で、非可換な項目を持つ特定の行列に対して、det(AB)=det(A)det(B)の関係の類推として成立する。特に、Lie代数glₙの表現論に関連し、CayleyのΩ過程（Ω）を介して、不変量ƒとその変形Ωƒとの関係を結びつけるために用いられる。
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(mathematics) An analog of the formula det(AB) = det(A) det(B), for certain matrices with noncommuting entries, related to the representation theory of the Lie algebra glₙ. It can be used to relate an invariant ƒ to the invariant Ωƒ, where Ω is Cayley's Ω process.
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Capelli's identity
When studying the invariants of polynomial representations of glₙ, Capelli's identity provides a noncommutative analogue of det(AB) = det(A) det(B) that relates an invariant f to Ωf via Cayley's Ω process.
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When studying the invariants of polynomial representations of glₙ, Capelli's identity provides a noncommutative analogue of det(AB) = det(A) det(B) that relates an invariant f to Ωf via Cayley's Ω process.
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