Re: matrix substitution--> arithmetization of Cayley table for Octonions
- To: mathgroup at smc.vnet.net
- Subject: [mg67653] Re: matrix substitution--> arithmetization of Cayley table for Octonions
- From: Roger Bagula <rlbagula at sbcglobal.net>
- Date: Mon, 3 Jul 2006 06:38:37 -0400 (EDT)
- References: <e665nv$n43$1@smc.vnet.net> <e7583n$l3s$1@smc.vnet.net> <e78411$fli$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
The substitution is to change a symbol into a number / weight:
{1, i , j , k, l , il, jl, kl}->{1,2,3,4,5,6,7,8}
(*http : // en.wikipedia.org/wiki/Octonion*)
(* Cayley Multiplication table*)
o = {{1, i , j , k, l , il, jl, kl},
{i, -1 , k , -j , il , -l , -kl , jl},
{j, -k , -1 , i , jl , kl , -l , -il},
{ k, j , -i , -1 , kl , -jl , il , -l},
{l, -il , -jl , -kl , -1 , i , j , k},
{il, l , -kl , jl , -i , -1 , -k , j},
{jl, kl , l , -il , -j , k, -1, -i},
{kl, -jl , il , l , -k , -j , i , -1}}
(* new matrix from table*)
on = o /. i -> 2 /. j -> 3 /. k -> 4 /. l -> 5 /. il -> 6 /. jl -> 7 /.
kl -> 8
MatrixForm[on]
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