Talk:Biquaternion

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[edit] Conflict of terminology

There seems to be a conflict of terminology with regards to the name biquaternion. Hamilton appears to have used the term to mean a quaternion with complex coefficients (i.e. C⊗H), while Clifford (in Preliminary Sketch of Biquaternions, 1873) uses the term to mean an algebra isomorphic to H⊕H, which follows the quaternions in the sequence of Clifford algebras:

R → C → H → H⊕H → ...

The complexified quaternions are not isomorphic to Clifford's biquaternions. This page presently discusses Hamilton's notion, while the German version of the page discuss's Clifford's notion. Some mention should be made of the conflict. I'm not sure which term is more commonly used. -- Fropuff 21:43, 19 February 2006 (UTC)

[edit] Clifford biquaternion

Since the structure of Clifford biquaternions is demonstrably different than the classical twentieth century concept of biquaternions used to develop the relativity transformations, the works of the Clifford algebraists on their biquaternion need a separate space. Rgdboer 01:35, 23 February 2006 (UTC)

Well okay; I'm not sure the name is standard, but I guess we have to disambig them somehow. At any rate we should probably mention the alternate meaning somewhere in the intro to this article.

Of course, Hamilton's biquaternions also form a Clifford algebra, just with the opposite signature from Clifford's biquaternions. They fit into the sequence

R → C^~ → H^~ → C⊗H → ...

with C^~ and H^~ being the split-complex numbers and split-quaternions respectively. -- Fropuff 04:01, 23 February 2006 (UTC)