Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 2 / 3 / d

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- Solution d

Solution

Use the multiplicativity rule for the cobraided bialgebra and

Δ b = a \otimes b + b \otimes d

:

r (a^{2}, b) = r (a, b_{(1)}) r (a, b_{(2)}) = r (a, a) r (a, b) + r (a, b) r (a, d) .

The generator table has

r (a, b) = 0

, so

r (a^{2} \otimes b) = 0.

Here the tensor notation means the value of the scalar form on the two displayed arguments, not multiplication within

M_{q} (2)

.

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