Notes for AKT-090924-2/0:36:01

Exercise. If $f\in {\mathcal {V}}_{n}$ and $g\in {\mathcal {V}}_{m}$ then $f\cdot g\in {\mathcal {V}}_{n+m}$ (as what one would expect by looking at degrees of polynomials) and $W_{f\cdot g}=m_{\mathbb {Q} }\circ (W_{f}\otimes W_{g})\circ \Delta$ where $(W_{f}\otimes W_{g})\circ \Delta :{\mathcal {A}}\rightarrow \mathbb {Q} \otimes \mathbb {Q}$ and $m_{\mathbb {Q} }$ is the multiplication of rationals.