• ## Re: [truenumber] lattice of a gauge group

(2)
• NextPrevious
• Dear Roger, About lack of elementary knowledge from Lie Groups is good sample http://en.wikipedia.org/wiki/SU(2) where we can read In mathematics, the special
Message 1 of 2 , Aug 1, 2006
View Source
• 0 Attachment
Dear Roger,
About lack of elementary knowledge from Lie Groups is good sample
"In mathematics, the special unitary group of degree n, denoted SU(n), is the group of n×n unitary matrices with unit determinant. The group operation is that of matrix multiplication. "
of course "The group operation isn't matrix multiplication"

Authors copy textes from another sources not understand these and counting nothing. Uses terms homomorphism etc to hidden lack of knowledge to count anything

General problem is that True Mathematicians like Sylvester, Cayley, Lie die long times upon ago and now are problems because no successors.

BEST WISHES
ARTUR

----- Original Message -----
From: Artur
Sent: Saturday, July 29, 2006 9:43 PM
Subject: Re: [truenumber] lattice of a gauge group

Dear Roger,
1) I don't mentioned that physical universe doesn't exist (but who now ?!).
2) SU(5) isn't anyone Clifford Algebra. Of course all Clifford Algebras have matrix representations and all of these are well know for me and are groups for classic multiplication of matrices but dimmensions are very high because Clifford indices e.g. CL(7,3) spoke only about number of generators and don't spoke about number of total elements which are closed for operation of multiplication matrices.

3) Anyone SU with exception SU(1) isn't group for classical multiplication of matrices and can't be because is not associative.
I can explained you this nuances on the simplest Special Unitary Group SU(2) which have matrix representation but is group not for multiplication * of matrices but for operation taking of commutator defined as [x*y-y*x]
If you take following representation:

X=(1/2){{i,0},{0,-i}}
Y=(1/2){{0,1},{1,0}}
Z=(1/2){{0,i},{i,0}}

Now let group operation will by [] defined as [x*y-y*x]
Cayley Table SU(2) is following
[] │ X   Y   Z
___________
X  │  0  Z   -Y
Y │-Z   0   X
Z  │Y  -X   0

Of course taking of commutator is one of possible representation vector multiplication SU(2)
and in this representation we can't count eigenvalues. In other repesentation these is possible and we discover ANOTHER WORLDS (or our World).

Problem is that people which working in Physic can't count eigenvalues in any SU algebra becuase mathematical knowledge isn't sufficient to do that. I doubt also very much that anyone recent Mathematician can help on this because I was check these personally with the best World Mathematicians from not associative algebras. All these persons are far away from counting eigenvalues in not associative algebras and nobody (person or institution) is interested this topic which is fundamental for Physics.

BEST WISHES
ARTUR

----- Original Message -----
Sent: Saturday, July 29, 2006 6:58 PM
Subject: [truenumber] lattice of a gauge group

Artur,

Here's it it breaks down logically:
1) the physical universe exists
2) there is a gauge group associated with the physics of the physical
universe
3) Number like groups of the Clifford algrebrs sort are the basis of
other groups
as the numbers make up all that is mathematics
4) we measure the physical universe using numbers
5) groups of numbers that form lattices that fill spaces are connected
to number based polynomials
that are connected to manifolds
6) the gauge group and some numerical polynomial representation of an
embedded manifold
determine a fundamental lattice for all the fields of the physical
universe, so that the space is filled
and the physics is covered [ equivalent to 2) logically]

So there have to be minimal irreducible polynomials for Clifford algebras
with beta integer like solutions.
Equivalent to saying Penrose tiles in two dimensions have equivalents
in higher dimensions.

It is like the
SU(5) -> U(1)*S(2)*S( 3)/ Z6
symmetry breaking of the "Standard Model" of physics.
I didn't make it up.
Dr. Thurston came up with the idea of Quaternion tilings.
I'm just trying to figure out how to compute it.
My approach is starting at the tiles we know best in complex dynamics:
Pisots.
Roger Bagula

Your message has been successfully submitted and would be delivered to recipients shortly.