Adel, thank you for the questions. Since you ask I will give you a potted history of how my work developed and you can compare with your own path.
As a PhD student I worked on Lattice Gauge Theories and wrote programs to do Monte Carlo calculations, much like the Buffon's needle trick except there are many more variables in the calculation.
I left academia but was still interested in doing some monte carlo simulations on my home computer (a Commodore Amiga) Full blown lattice gauge computations were out of the question but some people were looking at random triangulation models for quantum gravity and I wondered what would happen if it was simplified to just a random graph. I was conditioned to think about symmetries so I thought the permutation symmetry might be spontaneously broken to form an emergent spacetime.
I found that this was possible but only in contrived ways so I wondered in the adjacency matrix for the random graph could be generalised to a full random matrix so that the permutation symmetry $S_N$ becomes a matrix group like $SO(N)$ or $SU(N)$ which would allow the spacetime symmetry to be unified with gauge symmetry.
This was in 1987-1990. I had no internet or other way to look at other peoples research so I did not even know that there was a mathematical literature on random graphs and random matrices.
In 1992 I was working in France and had access to the internet so I found out about arXiv (as we now call it). I did a catch up on string theory and realised that my ideas of emergent spacetime could be relevant to what people were asking about spacetime in string theory and what happened to it in the "topological phase", so I worked on it some more and put some papers on arXiv about random graphs and random matrices with generalisations to include sypersymmetry.
While random matrices were interesting I saw that they were also limited. I felt that the ultimate model should have complete symmetry so that the field variables themselves are in one-to-one correspondence with the generators of the symmetry. For a matric model this would mean using a single matrix, but single matrix models do not have a rich enough structure, so I started to look at generalisations involving tensors in addition to the matrices. I wanted to produce a random model inspired by string field theory.
I thought I had done it in 1995 when I heard that an old friend Richard Borcherds had succeeded in using symmetry structures from string theory to prove the Moonshine conjectures so I showed him my string inspired symmetry algebras to ask if there could be a connection. He pointed out with a counterexample that my symmetry did not close. Luckily the counter-example made me realise the way to correct the problem and I published this on arXiv and the Int J Theor Phys.
The Lie algebras I had constructed for discrete strings were a form of necklace Lie algebra, but these were not known to me at the time so I did not use that term until later. That is probably why you cant find them in my work. see http://arxiv.org/abs/hep-th/9510042 http://arxiv.org/abs/hep-th/9609118
These papers generated a little interest at the time from people like Leonard Suskind who wrote to me to say that he was also looking at discrete strings while trying to solve the black hole information paradox. Soon after he published him Matrix Theory. Where I spoke of spacetime events he spoke of instatons so nobody noted the connection with my event-symmetry. Another group did play on the connection between the permutation symmetries and diffeomorphism invariance but there was never any mention or citation of my work so nobody follows the idea through to the necklace lie algebras.
Much later in 2006 the idea of quantum graphity arrived which reinvented the idea of random graphs using permutation symmetry. Again there was no reference back to my work so nobody followed to where I had taken the idea (Later they did give me a citation)
So for twenty years I have been sitting on this idea of Necklace Lie Algebras. The maths is very tidy. It falls into place naturally and can be generalised through an iterative process that I think is related to multiple quantisation. The complete symmetry is just what would be needed to formulate a holographic theory that everybody is puzzling over. I learnt that necklace lie algebras similar to mine are of interest to mathematicians. Even that the free lie algebra can be arranged into the form of a necklace lie algebra and there are ways of mapping this through iterated integration to spacetime. The amplituhedron also uses Yangian symmetries with a linear structure and they scratch their heads wondering how these might be extended to string theory.
So each year I write an FQXi essay and try to promote my ideas in different ways, but always everyone knocks it down and the winners are safer ideas with nothing very new or radical. I dont mind because I would rather write about what is meaningful to me than something safe and accepted that other people already agree with.
I think eventually people will see that necklace lie algebras, multiple quantisation, complete symmetry and all that fit in, perhaps in another twenty years time it will happen. From my experience so far I expect that when they do they will use a different language and a different interpretation and so they will not recognize the connection to my work even then. That is what happen when you work independently outside the system. I dont mind that. I am happy that I have known stuff for over twenty years that other people are still confused about and I may have another twenty years of it before they finally get it.
So my advise to you is keep working on your stuff yourself is nobody else will listen. Make sure your results are out there somewhere permanent and dont be disappointed if nobody joins in to work on it with you. Just enjoy the pleasure of having a different way of looking at things that others cant see yet.
