Lie-Algebra of type E6

The purpose of this project is to systematically develop a method to construct chevalley algebra for type E6 over galios field F2. The importance of this study is that it will lead to the construction of the embedding 3 F 22 <3. E(2) < 3. E6 (4) <= GL (27,4), where [2] R Wilson will be mentioned that there is a triple cover 3. Fi 22 generated by 3510 transpositions. This has a 27- dimensional representational over galios field f4. This representation is unitary in the sense that its dual is equivalent to the representation obtained by applying the field of auto morphism. In other words 3.F i22 embeds in SU27 (2). This embedding was explicitly constructed by Richard Parker. It turns out that 3 Fi22 contains a proper triple cover 3. Omega7 (3) of the orthogonal group Omega 7(3), and in turns 3. Omega7 (3) counting 3. G2 (3). Thus one can obtain two more of the exceptional cover somr groups of lie type from 3. Fi 22.3.