Timeline for Definition of Pin groups?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 4, 2022 at 21:35 | comment | added | Eric | From what I can tell, $\operatorname{Pin'}(q) = \operatorname{Pin}(-q)$ and vice versa | |
| Oct 3, 2016 at 16:49 | comment | added | user21230 | @TomDeMedts: Probably, I am more intuitionist. When you publish something, surely you should use definitions understandable for others. But when you're doing research you can leave some details to clarify later on. For example it is enough to understand that Pin is double cover of $O_n$. Besides it is not the first neither the last situation in mathematics that there are several definitions of the same thing. On school level, I have learned that 0 is not natural number. Now I hear that in most western countries 0 is natural number. In Poland it is not settled, so on exams 0 is treated separate | |
| Oct 3, 2016 at 16:15 | comment | added | nfdc23 | @TomDeMedts: Certainly definitions are very important, but one's choice of definitions are best guided by what one wishes to do with them. Marek Mitros is pointing that the author doesn't give any indication about what (s)he wishes to do with Pin groups, and that consequently it is not possible to adequately answer the question (beyond that one has to be clear on one's choice). The literature has multiple conventions because there are many purposes for Pin groups (and allowing algebraic groups or group schemes rather than Lie or abstract groups makes it even more abundant!). | |
| Oct 3, 2016 at 15:03 | comment | added | Tom De Medts | @MarekMitros: "For me the definition of things is less important." -- What? How can you communicate about mathematics if you don't have precise definitions? The OP points out exactly that having different definitions for the same notion can be very confusing, and should be avoided as much as possible. | |
| Oct 3, 2016 at 9:36 | comment | added | user21230 | Personally I read only some works of Pertti Lounesto from mentioned above. For me the definition of things is less important. More important is what would you like to investigate on. Then take your favourite definition and go ahead. For me Spin group is interesting enough, because it is double cover of $SO_n$. I don't know what is the advantage of Pin groups. Logically it should be double cover of $O_n$. That would give the same reason for adding letter $S$ in front of the name. That explanation is given in wikipedia article for Pin group and I like this. "This joke is due to J-P. Serre" ... | |
| Oct 3, 2016 at 2:39 | review | First posts | |||
| Oct 3, 2016 at 3:16 | |||||
| Oct 3, 2016 at 2:34 | history | asked | Ragnar | CC BY-SA 3.0 |