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 [math]\displaystyle{ {\mathcal A}(\uparrow) }[/math].
• PBW for [math]\displaystyle{ {\mathcal A}(\uparrow_n) }[/math].
• The VS structure on [math]\displaystyle{ {\mathcal A}(\uparrow_\star) }[/math] and on [math]\displaystyle{ {\mathcal B}_\star }[/math].
• The algebra structure on [math]\displaystyle{ {\mathcal A} }[/math] and [math]\displaystyle{ {\mathcal B} }[/math].
• The graded representations [math]\displaystyle{ {\mathcal E}_k }[/math] and their decompositions into irreducibles:

From Dror's Some Computations Related to Vassiliev Invariants.

• Coloured stickers and tensor products over [math]\displaystyle{ S_k }[/math].
• Computing the homology.