"One can construct the (compact form of the) E8 group as the automorphism group of the corresponding e8 Lie algebra. This algebra has a 120-dimensional subalgebra so(16) generated by Jij as well as 128 new generators Qa that transform as a Weyl–Majorana spinor of spin(16). These statements determine the commutators

as well as

while the remaining commutator (not anticommutator!) is defined as

It is then possible to check that the Jacobi identity is satisfied.
Geometry[edit source | editbeta]

The compact real form of E8 is the isometry group of the 128-dimensional exceptional compact Riemannian symmetric space EVIII (in Cartan's classification). It is known informally as the "octooctonionic projective plane" because it can be built using an algebra that is the tensor product of the octonions with themselves, and is also known as aRosenfeld projective plane, though it does not obey the usual axioms of a projective plane. This can be seen systematically using a construction known as the magic square, due to Hans Freudenthal and Jacques Tits (Landsberg & Manivel 2001).
Applications[edit source | editbeta]

The E8 Lie group has applications in theoretical physics, in particular in string theory and supergravity. E8×E8 is the gauge group of one of the two types of heterotic stringand is one of two anomaly-free gauge groups that can be coupled to the N = 1 supergravity in 10 dimensions. E8 is the U-duality group of supergravity on an eight-torus (in its split form).
One way to incorporate the standard model of particle physics into heterotic string theory is the symmetry breaking of E8 to its maximal subalgebra SU(3)×E6.
In 1982, Michael Freedman used the E8 lattice to construct an example of a topological 4-manifold, the E8 manifold, which has no smooth structure.
Antony Garrett Lisi's incomplete theory "An Exceptionally Simple Theory of Everything" attempts to describe all known fundamental interactions in physics as part of the E8Lie algebra.[6][7]
R. Coldea, D. A. Tennant, and E. M. Wheeler et al. (2010) reported that in an experiment with a cobalt-niobium crystal, under certain physical conditions the electron spins in it exhibited two of the 8 peaks related to E8 predicted by Zamolodchikov (1989) .[8] [9]

ask Saul-Paul Sirag & Tony Smith

The EM U1, weak SU2 & strong SU3 are LOCALLY gauged internal symmetry groups in the fiber space whose base is 4D space-time.

In contrast T4 is a symmetry group for the base 4D space-time.

In order to get a consistent gravity gauge theory we need to localize the Poincare symmetry group of Einstein's 1905 SR and this gives both curvature and torsion as independent dynamical fields. Einstein's 1915 plain vanilla GR ad hoc constrains the torsion to be zero.

Hagen Kleinert showed that torsion is a dislocation defect field in a world crystal lattice.

Curvature is the disinclination defect field.

Hammond et-al say that quantum spin generates dynamical torsion.

There is controversy over propagating torsion waves (e.g. Gennady Shipov in Moscow) as well as coupling of torsion with orbital angular momentum of matter fields as well as their quantum spin.

On Sep 18, 2013, at 6:21 PM, David Mathes <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:

T4 == U(1) X SU(2) X SU(3) for flat space...?

Extended with Higgs plus, one might even simplify it to

T4 = E8?


From: JACK SARFATTI <This email address is being protected from spambots. You need JavaScript enabled to view it.>
To: art wagner <This email address is being protected from spambots. You need JavaScript enabled to view it.

Sent: Wednesday, September 18, 2013 6:12 PM
Subject: Re: Chromogravity & An Important Experiment

"Gravitational field is the manifestation of space-time translational (T4) gauge symmetry, which enables gravitational interaction to be unified with the strong and the electroweak interactions. Such a total-unified model is based on a gen- eralized Yang-Mills framework in flat space-time."

I have said this for many years now.

On Sep 18, 2013, at 6:00 PM, art wagner <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:

E8 (mathematics) - Wikipedia, the free encyclopedia
In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattic