[seqfan] Re: detective work related to Creighton Dement's \\\"Floretions\\\"

[Jonathan Post]

Wasn't there a comment that identified Floretions as a specific
nonassociative algebra, in a way that explains where the complex,
quaternionic, and octonionic structures come from?

On Fri, Nov 20, 2009 at 2:49 PM, Creighton Kenneth Dement
<creighton.k.dement at mail.uni-oldenburg.de> wrote:
> Joerg wrote:
>> Get rid of random letters for the components!
>> As it is, noone will ever dig through this messy notation.
>
> Getting rid of the "random letters for the components" is the whole
> purpose of introducting the projection operators
> ibase(X), jbase(X), etc. ...
>
> What is your point other than making jokes? I know you didn't just look at
> this stuff today, because you have kindly offered to help me before (if my
> memory serves me correctly) and I didn't hear any of this then.
>
>> Does your algebra contain (e.g.) complex numbers, quaternions, octonions?
>
> If "my algebra" contains quaternions, which I believe I mentioned only a
> few days ago on this seqfan list, it certainly contains complex numbers.
>
> Sincerely,
> Creighton
>
>
>> * Creighton Kenneth Dement <creighton.k.dement at mail.uni-oldenburg.de> [Nov
>> 21. 2009 07:32]:
>>> [...]
>>
>>>
>>> Here are the very basics which should be any such page.
>>>
>>> Let X = A'i  + B'j + C'k + Di' + Ej' + Fk' + G'ii' + H'jj' + I'kk' +
>>> J'ij' + K'ik' + L'ji' + M'jk' + N'ki' + O'kj' + P'ee'
>>>
>>> and Y = a'i  + b'j + c'k + di' + ej' + fk' + g'ii' + h'jj' + i'kk' +
>>> j'ij' + k'ik' + l'ji' + m'jk' + n'ki' + o'kj' + p'ee'
>>>
>>> Then
>>>
>>> ibase(X) = A
>>> jbase(X) = B
>>> kbase(X) = C
>>> basei(X) = D
>>> basej(X) = E
>>> basek(X) = F
>>> ibasei(X) = G
>>> jbasej(X) = H
>>
>>  [about here my brain starts bleeding]
>>
>>> kbasek(X) = I
>>> ibasej(X) = J
>>> ibasek(X) = K
>>> jbasei(X) = L
>>> jbasek(X) = M
>>> kbasei(X) = N
>>> kbasej(X) = O
>>> tes(X) = P
>>
>> Oh dear, _this_ is obfuscation in perfection.
>> What about the scheme used in sect.37.14, p.831ff
>> of http://www.jjj.de/fxt/#fxtbook  ?
>> It's an algebra, dammit.
>>
>> Get rid of random letters for the components!
>> As it is, noone will ever dig through this messy notation.
>>
>>
>>> [...rather random looking functions...]
>>
>> Can the specific definition be somehow motivated?
>>
>>
>>>
>>>
>>> X*Y =
>>>
>>> (Pa - Dg - Ho + Im - Fk - Ej + Oh - Cb - Gd + Nl - Je - Kf - Mi + Ap +
>>> Bc
>>> - Ln)'i
>>>
>>> [...etc...]
>>
>> Does your algebra contain (e.g.) complex numbers, quaternions, octonions?
>> Is it even isomorphic to the sedenions or some Clifford algebra?
>>
>> What are the sub-algebras (if it has any)?
>>
>> Is it (or are any sub-algebras) associative or commutative?
>>
>> Zero-divisors?
>>
>>
>>> [...]
>>
>> btw. your old domain is available for registration,
>> you may want to (re-)register it.
>>
>> cheers,   jj
>>
>> P.S.: a grouchy German is a Sauer-Kraut
>>
>>
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>>
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>>
>
>
>
>
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