 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2007/iii/paper-2/3/d/solution

Codex  0 Created 2026-10-03 Updated 2026-10-14

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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