Talk:Spin group

message: Should that be Spin+(2,2) = SO(2,2), rather than just Spin(2,2)? Tom Huckstep 10:54, 28 August 2007 (UTC)
thread_title: Spin+

message: This page needs to be cleaned up, and in particular needs some references.  I haven't dealt much with Spin groups myself, but I know for instance that Spin(2)=U(1)=O(2) is just plain wrong.  U(1) is *not* the same as O(2), but *is* the same as SO(2).  Also, this is not a double cover, which seems to violate the definition at the top -- however, the comment towards the bottom of the page (which *does* say Spin(2)=SO(2)) says that there are special exceptions, when the fundamental group does not contain Z_2.  It seems, therefore, that the definition is probably incorrect, and the "accidental isomorphisms" section contains at least one error.  Could an expert please clear this up, and add at least one good reference? 131.215.118.194 01:03, 11 September 2007 (UTC)
thread_title: SO vs O

message: Have reworked and corrected the spin group article, added separate sections for indefinite signature and topology. Let me know if there still are errors in the article.
Cheesefondue 11:47, 13 October 2007 (UTC)
replies: text: The new version looks much better, thanks. I guess some choice needs be made about the connectivity of Spin(p,q). All but one of the references I have define Spin(p,q) to be a double cover of SO(p,q) rather than SO+(p,q), so I would lean towards this convention. I am, however, aware of the reasons for not wanting to do so. Probably both conventions should be stated and explained at some point. -- Fropuff 02:10, 14 October 2007 (UTC)
thread_title:  Changes 

message: I'm a bit befuddled by the exact sequence definition.  Is there a more constructive definition of Spin(n)?
On a related note, is Spin(n) the unit elements of the even subalgebra of Cl(n)?
Thanks, 70.116.91.46 (talk) 04:36, 12 March 2012 (UTC)
thread_title:  constructive definition? 

message: What is meant by $Spin(2)=U(1)$ and te others? 
Surely they are not isomorph as topological groups, since $Spin(2)$ as to be simply connected,
while $U(1)$ is not...
Moreover the symbol $=$ shouldn't be used here $\simeq$ is more apropriate, IF the groups
are homoeomorph  — Preceding unsigned comment added by 212.23.103.73 (talk) 11:54, 17 May 2013 (UTC)
replies: text: Indeed,  is the only case where  is not simply connected. You apparently do not understand that the Spin group has not necessarily to be the universal cover of the orthogonal group. It is a double cover (topology), which may or may not be universal. Incnis Mrsi (talk) 12:45, 17 May 2013 (UTC)
replies: text: In fact, for , ≈≈. Hence, ≈≈≈   is not the trivial group } which contains only the unit element.Mgvongoeden (talk) 16:18, 18 May 2013 (UTC)
thread_title:  Unclear 

message: The reference to Varadarajan (p.208) states that for p and q both even the center of \operatorname{Spin}(p,q) coincides with that of \operatorname{Spin}(p+q,\mathbf{C}) then makes a mistake when giving the explicit answer.  Namely, it is \mathrm{Z}_4 for p+q=4k+2 and \mathrm{Z}_2\oplus\mathrm{Z}_2 for p+q=4k. I'm correcting that now in the article. 69.141.211.196 (talk) 03:34, 5 November 2016 (UTC)
thread_title:  Center of Spin group 

message: And IMHO nothing special should be written on this kind of construction besides that it’s the quotient algebra of tensor algebra. Which ideals are suitable? Again, topical to tensor algebra. Incnis Mrsi (talk) 18:51, 4 May 2019 (UTC)
replies: text: @67.198.37.16: this talk page is about the article Spin group!  now have {tensor,quotient,Clifford} algebra and a lot of other links from here in my watchlist. Please, go elsewhere with proposals not directly related to editing “Spin group”. Incnis Mrsi (talk) 20:19, 4 May 2019 (UTC)

text: The redirect quotient associative algebra is online. Incnis Mrsi (talk) 09:14, 7 May 2019 (UTC)
thread_title:  Quotient algebra