# Talk:Split-biquaternion

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Field: Algebra (historical)

## Appropriation of nomenclature

W.K.Clifford wrote the following footnote to justify use of the term biquaternion:

Hamilton's biquaternion is quaternion with complex coefficients; but it is convenient (as Prof. Pierce remarks) to suppose from the beginning that all scalars may be complex. As the word is no longer wanted in its old meaning, I have made bold to use it in a new one.(footnote pp. 188-9)

Actually the word is wanted in its old meaning. Rgdboer 20:54, 14 April 2006 (UTC)

## Move explained

The term "Clifford biquaternion" is used for both dual quaternions (see Rooney) and for the split-biquaternion ring. This ambiguity is being divided by the natural inclusion of the descriptor (split or dual) of the coefficient ring in each case.Rgdboer (talk) 01:25, 30 March 2008 (UTC)

## Even Subalgebra

It would also be nice that the article noted somewhere that split-biquaternions arise as the even sub-algebra of 4-dimensional real Clifford algebra, ${\displaystyle Cl_{4}^{+}(\mathbb {R} )}$. It is the spin group of euclidean 4-D space, so to speak, which is as we know, representable by two ordinary quaternions, one from the left and one from the right. -- 78.54.51.242 (talk) 21:06, 13 January 2012 (UTC)

Please provide a reference and this sub-algebra will be so identified.Rgdboer (talk) 21:31, 10 December 2013 (UTC)

## Synonym Clifford biquaternion

In the "Synonyms" section, it says "Clifford biquaternion" was used by Joly (1902) and van der Waerden (1985). But van der Waerden (on p. 188, as cited at the end of the article) just says that Clifford introduced two different types of biquaternions (different from Hamilton's), and later calls them once: Cliffords first and second kind of biquaternions. (This agrees with Rgdboer's comment below, under "Move explained".) Van der Waerden didn't really coin a name and use it afterwards repeatedly. I suggest to remove the reference to van der Waerden. Apart from this minor point, including a "Synonyms" section is very commendable, and I thank the person who did it for the effort and research put into it. — Preceding unsigned comment added by Herbmuell (talkcontribs) 04:29, 10 December 2013 (UTC)

Thank you for your kind comment. While it is true that van der Waerden did not expand on this algebra, he did make his statement about its origin with Clifford's writing, and this is noteworthy. Thus retention of this important reference to hypercomplex numbers generally serves to support knowledge of the subject of this article, though the eponym is not highlighted.Rgdboer (talk) 21:31, 10 December 2013 (UTC)