Knot at Lunch on December 12 2007 - Revision history

Drorbn at 18:28, 12 December 2007

2007-12-12T18:28:49Z

← Older revision		Revision as of 14:28, 12 December 2007
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	==Bone Soup==		==Bone Soup==
	Let <math>n</math> be a natural number and let <math>R={\mathbb Z}[x_1,\ldots,x_n]</math> be the ring of polynomials in <math>n</math> variables <math>x_1,\ldots,x_n</math>. ~~Let~~ <math>B_n</math> be the <math>R</math>-module generated by symbols <math>B_{ij;kl}</math> (the "bones") where <math>1\leq i,j,k,l\leq n</math>, subject to the relations:		Let <math>n</math> be a natural number and let <math>R={\mathbb Z}[x_1,\ldots,x_n]</math> be the ring of polynomials in <math>n</math> variables <math>x_1,\ldots,x_n</math>. The <math>n</math>'th bone soup module <math>B_n</math> is the <math>R</math>-module generated by symbols <math>B_{ij;kl}</math> (the "bones") where <math>1\leq i,j,k,l\leq n</math>, subject to the relations:
	* <math>B_{ij;kl}=B_{kl;ij}=-B_{ji;kl}=-B_{ij;lk}</math>.		* <math>B_{ij;kl}=B_{kl;ij}=-B_{ji;kl}=-B_{ij;lk}</math>.
	* <math>x_mB_{ij;kl}-x_jB_{im;kl}+x_iB_{jm;kl}=0</math>.		* <math>x_mB_{ij;kl}-x_jB_{im;kl}+x_iB_{jm;kl}=0</math>.

Drorbn at 17:06, 12 December 2007

2007-12-12T17:06:06Z

← Older revision		Revision as of 13:06, 12 December 2007
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	==Bone Soup==		==Bone Soup==
	Let <math>n</math> be a natural number and let <math>R={\mathbb Z}[x_1,\ldots,x_n]</math> be the ring of polynomials on <math>n</math> ~~generators~~ <math>x_1,\ldots,x_n</math>. Let <math>B_n</math> be the <math>R</math>-module generated by symbols <math>B_{ij;kl}</math> (the "bones") where <math>1\leq i,j,k,l\leq n</math>, subject to the relations:		Let <math>n</math> be a natural number and let <math>R={\mathbb Z}[x_1,\ldots,x_n]</math> be the ring of polynomials in <math>n</math> variables <math>x_1,\ldots,x_n</math>. Let <math>B_n</math> be the <math>R</math>-module generated by symbols <math>B_{ij;kl}</math> (the "bones") where <math>1\leq i,j,k,l\leq n</math>, subject to the relations:
	* <math>B_{ij;kl}=B_{kl;ij}=-B_{ji;kl}=-B_{ij;lk}</math>.		* <math>B_{ij;kl}=B_{kl;ij}=-B_{ji;kl}=-B_{ij;lk}</math>.
	* <math>x_mB_{ij;kl}-x_jB_{im;kl}+x_iB_{jm;kl}=0</math>.		* <math>x_mB_{ij;kl}-x_jB_{im;kl}+x_iB_{jm;kl}=0</math>.

Drorbn at 16:24, 12 December 2007

2007-12-12T16:24:29Z

← Older revision		Revision as of 12:24, 12 December 2007
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	'''Question 1.''' Can you find a simple basis for <math>B_n</math>?		'''Question 1.''' Can you find a simple basis for <math>B_n</math>?

	'''Question 2.''' Is <math>B_n</math> related to curvature tensors and Bianchi identities?		'''Question 2.''' Is <math>B_n</math> related to curvature tensors and Bianchi identities?

Drorbn at 16:24, 12 December 2007

2007-12-12T16:24:15Z

← Older revision		Revision as of 12:24, 12 December 2007
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	Dror.		Dror.

			==Bone Soup==
			Let <math>n</math> be a natural number and let <math>R={\mathbb Z}[x_1,\ldots,x_n]</math> be the ring of polynomials on <math>n</math> generators <math>x_1,\ldots,x_n</math>. Let <math>B_n</math> be the <math>R</math>-module generated by symbols <math>B_{ij;kl}</math> (the "bones") where <math>1\leq i,j,k,l\leq n</math>, subject to the relations:
			* <math>B_{ij;kl}=B_{kl;ij}=-B_{ji;kl}=-B_{ij;lk}</math>.
			* <math>x_mB_{ij;kl}-x_jB_{im;kl}+x_iB_{jm;kl}=0</math>.

			'''Question 1.''' Can you find a simple basis for <math>B_n</math>?
			'''Question 2.''' Is <math>B_n</math> related to curvature tensors and Bianchi identities?

Drorbn at 15:53, 10 December 2007

2007-12-10T15:53:37Z

New page

{{KAL/Navigation}}

==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 <span class="plainlinks">{{SERVER}}/drorbn/index.php?title={{PAGENAMEE}}</span>.

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.