An answer on an important reply: The non-commutative octonions!

[PC]

Some bright guy asked, why I just didn't have any problems with the
non-commutative octonions.

The answer is this: I've been keeping everything on a real form, like
this:
a + b j + c k + d l + e i + f i j + g i k + h i l, where a to h are
real constants. Then there will really not be any problems with
multiplication. -Ok, we get basically up to 64 terms (8x8), but that
should really be possible to handle. -I do never replace a*b with b*a,
if we see both a and b as octonian numbers, that's the intentition.
Should you find, that I have been doing some error, just let me know.

The same 'trick' is often used even with the normal complex numbers:
Always write z = a + i b: where both a and b are real numbers; You can
actually very easily handle a multiplication of two numbers, because
it will never give more than just 4 terms.

Honestly, I have been reading Baez's pages on octonions (http://
math.ucr.edu/home/baez/octonions/), and that's really fine material. -
But I still think that I can actually 'tame' these octonions in a
practical case: Just keep the numbers a-h real, then you can actually
handle the algebra in practice.

Of course, I would like to have a look at sites like "http://
www.quaternions.com/", but unf, the link doesn't work for me at the
moment. Why?- Otherwise we just share the same interest, I would
say...

Last to say: Sorry, my forum, the PSR-HA-forum is NOT completely
finished. -Maybe I did actually published my results in SPR a bit to
early...You could be right, when saying that there is basically
nothing at my site at the moment.

But 1 x promise: I will be back soon... :-)

Rgds,
Peter C

_________________________
Ps. I use j,k,l for the quaternions and i,j,k,l (1,j,k,l,i,ij,ik,il)
for the octonians, even though I know that this is not the standard
notation. I'm sorry If it's just disturbing.

Pps. Why I open my own forum is basically because I do not wan't to
irritate people in sci.math, sci.math.research, sci.physics,
sci.physics.relativity and sci.physics.research with my postings. I
think that writing in my own forum would just be "proper conduct" for
the sci-groups, because I know that my ideas are not what people would
call "standard theory"...