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05-22-2006, 02:59 PM
relativistic and Lie groups
The following list of web links contains topics discussing the different varieties of group used in the formulation of physical theories:

http://en.wikipedia.org/wiki/Category:Lie_groups and
http://en.wikipedia.org/wiki/Lorentz_group and http://en.wikipedia.org/wiki/Poincare_group

The question is which of these could describe the topologies of the following image?

Attachment 248

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05-22-2006, 04:41 PM
Re: relativistic and Lie groups
What if the topology which should describe those images is not yet invented? What characteristics should it have?
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05-23-2006, 01:01 PM
Re: relativistic and Lie groups
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Originally Posted by GUILLE
What if the topology which should describe those images is not yet invented?
The topology is known as a doubly twisted Möbius strip. I am still not sure about the Lie group representations although I used Hadamard matrices and these form a Hadamard group which are not differentiable or meaning not one to one correspondence but many to many correspondence.
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05-23-2006, 05:48 PM
Re: relativistic and Lie groups
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Originally Posted by AntonioLao
The topology is known as a doubly twisted Möbius strip. I am still not sure about the Lie group representations although I used Hadamard matrices and these form a Hadamard group which are not differentiable or meaning not one to one correspondence but many to many correspondence.
Many to many correspondence is seen a lot in permutation mathematics. Do you have an equation of the sort 2n! or something to represent that many to many correspondence?
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05-25-2006, 06:34 PM
Re: relativistic and Lie groups
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Originally Posted by GUILLE
Do you have an equation of the sort 2n! or something to represent that many to many correspondence?
No. I don't have any such equation. But I think many to many correspondence must in some ways related to non-associative algebra.
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05-25-2006, 07:47 PM
Re: relativistic and Lie groups
The following is an information link to non-associative algebra http://en.wikipedia.org/wiki/Categor...iative_algebra
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