Knot at Lunch on December 12 2007

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Dear Knot at Lunch People,

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

As always, please bring brown-bag lunch and fresh ideas. This is break time, and I expect relatively low attendance. So whatever we will do, it will be light and easy.

Further information about this meeting will/may appear at

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.



Bone Soup

Let n be a natural number and let R={\mathbb Z}[x_1,\ldots,x_n] be the ring of polynomials in n variables x_1,\ldots,x_n. The n'th bone soup module B_n is the R-module generated by symbols B_{ij;kl} (the "bones") where 1\leq i,j,k,l\leq n, subject to the relations:

  • B_{ij;kl}=B_{kl;ij}=-B_{ji;kl}=-B_{ij;lk}.
  • x_mB_{ij;kl}-x_jB_{im;kl}+x_iB_{jm;kl}=0.

Question 1. Can you find a simple basis for B_n?

Question 2. Is B_n related to curvature tensors and Bianchi identities?