Talk:Para-quaternion

message: The structure identified in this article is the same as the coquaternion ring originated and named by James Cockle. No reference is given for the isomorphism asserted. The reference linked is too technical to be of use by the non-expert. The assertion of use of para-quaternions in string theory is not backed-up. Should this page be retained in Wikipedia ?
:Rgdboer 23:58, 21 January 2007 (UTC)
replies: text: It looks like we have yet another candidate for the same thing ... Oh my ... Let's hope Wikipedia will at some time have a good reference across all those terms. Contained in Lie and Clifford algebra, I vote for merging all the split-/para-/hyperbolic-/co-quaternions into Coquaternion, and there make a section that lists, in the order of their re-invention, the isomorphism and potential differences in their definition. I believe that would be convincing encyclopedic content. Thanks, Jens Koeplinger 01:45, 20 May 2007 (UTC)
replies: text: Agree. As long as this section is clear and easy to find, it's the best. Right now the Coquaternion article is overloaded with content, and I don't have the editing skills required to make this merge cleanly and succintly. And if the merge is done in a careless way, it will destroy the value of all merged articles. Tiphareth 15:05, 20 May 2007 (UTC)
replies: text: Uh oh, I see work coming my way; it's my declared interest in making the many different algebras more easily accessible In Wikipedia, and it might be time now to live-up to my promises :) ... It's a terminology mess out there, but general popularity of algebras appears to be on the rise, and I want to make sure we represent in Wikipedia the lines between what's already invented, what's serious, what's useful, and what is pseudoscience ... In the next weeks I'll look at some well-written articles, how they're structured, and try to come up with an improvement to several algebra-related articles we already have. We've gotten much good additional content recently from Jheald, and the only thing I'd like to have is relations of some of these algebras to Lie algebras. I'll go and ask around who may be interested in providing isomorphisms or classifications (any help is appreciated). Thanks, Jens Koeplinger 15:33, 20 May 2007 (UTC)
replies: text: Great! Keep in mind that at some point the articles on para-quaternionic geometry (manifolds and related structures) will be added, so the links to the algebra and its relations should remain accessible. Regarding the hypercomplex algebra set-up, I think the Clifford algebra approach is the clearest and most up-to-date. Here are the links that I found very useful: 1, 2, 3. Also, please keep this talk page for history. Tiphareth 16:57, 20 May 2007 (UTC)
replies: text: I've started merging this material into split-quaternion. I agree that the latter needs much rewriting, and have commented on the Lie theory on the talk page. I will need the help promised above to complete the merge in a form which everyone will find satisfactory. This page will become a redirect, and hence its talk page history will be preserved. Geometry guy 12:17, 8 June 2007 (UTC)

text: Rgdboer 22:08, 27 January 2007 (UTC)
thread_title: Relation with coquaternions

message: I've added a merge tag.  There really ought only to be one article covering all uses of this object, not two. Jheald 20:06, 29 March 2007 (UTC)
replies: text: Agree with Jheald. We cannot have two articles on the same topic and there now seems to be agreement on this in the section above. I have merged the information in this article into split-quaternion with the intention of replacing it by a redirect. If the emphasis in the latter article is unsatisfactory, the solution is to update it, not to create a separate article. Geometry guy 12:05, 8 June 2007 (UTC)
thread_title:  Merge tag added 

message: One curiosity:
The paraquaternions are defined with ijk = -1, so k= -ij.
The coquaternions are defined with k = +ij, so ijk = +1.
It still works out to be the same algebra, just k has had a sign flip. Jheald 20:13, 29 March 2007 (UTC)
thread_title:  Sign convention