Knot at Lunch on December 12 2007

From Drorbn
Jump to: navigation, search

Invitation

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 http://www.drorbn.net/drorbn/index.php?title=Knot_at_Lunch_on_December_12_2007.

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.

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?