07-1352/Class Notes for March 27

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In Preparation

The information below is preliminary and cannot be trusted! (v)

Today's Agenda.

• Decisions regarding student presentations.
• PBW for ${\mathcal A}(\uparrow)$.
• PBW for ${\mathcal A}(\uparrow_n)$.
• The VS structure on ${\mathcal A}(\uparrow_\star)$ and on ${\mathcal B}_\star$.
• The algebra structure on ${\mathcal A}$ and ${\mathcal B}$.
• The graded representations ${\mathcal E}_k$ and their decompositions into irreducibles:

From Dror's Some Computations Related to Vassiliev Invariants.

• Coloured stickers and tensor products over $S_k$.
• Computing the homology.