Knot at Lunch on February 20 2008

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Invitation

Dear Knot at Lunch People,

We will have our next lunch on Wednesday February 20, at the usual place, Bahen 6180, at 12 noon.

As always, please bring brown-bag lunch and fresh ideas. The agenda: we may talk a bit about the infinitesimal side of Artin's theorem, or we may talk about something else. We will also need to decide whether we want to hold a "Thomas Fiedler Marathon" for a week sometime in June, for work in the spirit of the page "Dror Bar-Natan: Odds, Ends, Unfinished: Some One Parameter Knot Theory Computations"; if you want to know what this means, you'll have to come to lunch on time, for this will likely be the first topic we will discuss!

Further information about this meeting will/may appear at https://drorbn.net/drorbn/index.php?title=Knot_at_Lunch_on_February_20_2008.

As always, if you know anyone I should add to this mailing list or if you wish to be removed from this mailing list please let me know. To prevent junk accumulation in mailboxes, I will actively remove inactive people unless they request otherwise.

Best,

Dror.

The Proposed Thomas Fiedler Marathon

For	Against
We'll learn about his "one-parameter knot theory". We'll get some practical Hecke algebra experience, and gain faster HOMFLY programs. We'll get to play a bit with knot-theoretic programming. We'll get to experiment with instant math logging. We may discover something new.	The subject matter is not directly related to algebraic knot theory and/or knot theoretic algebra. It will cost us a week (a full week, not just the weekly meeting!). We may find at the end that mathematically speaking, it was all a waste of time.

Possible Agenda

• Infinitesimal Artin - derivations on free Lie algebras.
  • Derivations, tangential derivations, special derivations (see BBS/Alekseev-080116-162451.jpg).
  • Drinfel'd's theorem on special derivations (see Drinfel'd's On quasitriangular Quasi-Hopf algebras and a group closely connected with $\operatorname {Gal} ({\bar {\mathbb {Q}}}/{\mathbb {Q}})$, Leningrad Math. J. 2 (1991) 829-860, though I wouldn't be surprised if the theorem is actually older).
  • Can you prove that ${\mathcal {A}}^{\mbox{hor}}$ injects into ${\mathcal {A}}^{\mbox{trees}}$?
  • The VS structure on several kinds of algebras of derivations. As always, can you find associators?
  • The Alekseev-Torossian "divergence" (BBS/Alekseev-080121-093327.jpg).