| 1. | The bilinearity of the product follows immediately from the bilinearity of multiplication in.
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| 2. | The bilinearity of the product follows immediately from the bilinearity of multiplication in.
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| 3. | The first two conditions imply bilinearity.
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| 4. | In bilinearity ), so this distinction doesn't arise when considering real or complex Lie algebras.
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| 5. | Which is precisely preservation of the bilinear form which implies ( by linearity of and bilinearity of the form ) that is satisfied.
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| 6. | By the bilinearity of the pairings, the two expressions are equal if and only if ab = c modulo the order of P.
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| 7. | *PM : bilinearity and commutative rings, id = 9777 new !-- WP guess : bilinearity and commutative rings-- Status:
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| 8. | *PM : bilinearity and commutative rings, id = 9777 new !-- WP guess : bilinearity and commutative rings-- Status:
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| 9. | In summary, a Lie algebra is defined as a vector space " V " over a bilinearity, alternatization, and the Jacobi identity.
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