E6 matrix representation

[Marek Mitros]

I am looking for matrix representation of exceptional Lie algebras.

Has anyone knows where I can find construction of E6 Lie group or Lie algebra ? This exceptional Lie group can be embedded in SO(27). There are useful notes on page http://www.7stones.com/Homepage/octotut15.html
but this is too little for me to find the base of the lie algebra.

I was able to construct base of the f4 lie algebra using
1) Dixon's page mentioned above
2) Matsushima work from 1952
I has also used CLICAL of Pertti Lounesto and self-made program for commuting elements in so(n).

Algebra f4 is subalgebra of so(26).
Algebra e6 is subalgebra of so(27).
Algebra e7 is subalgebra of so(56).
Finally e8 is subalgebra of so(248).

I have already achieved following.
Definition:
h3(C*O) = {x belongs to M3(C*O): x*=x}
sa3(C*O) = {x belongs to M3(C*O): x*=-x;tr x = 0}

Define e6 as derivation of algebra h3(C*O). This means group E6 is automorfizms of h3(C*O). In Baez work we have:
e6 = Der O + sa3(C*O)

For element x from sa3(C*O) we define derivation Dx acting on h3 by formula
Dx(y) = xy - yx

I can find su3 and so8 this way but in this presentation h3(C*O) is 16*3+3*8 = 72-dimensional. I don't know how to map su3 found into so(27).

Regards,
Marek Mitros