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.