Timeline for Spin group as an automorphism group
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 10, 2014 at 14:00 | answer | added | Niels | timeline score: 2 | |
| Jul 30, 2013 at 16:34 | vote | accept | Mikhail Borovoi | ||
| Jul 30, 2013 at 14:17 | answer | added | Keerthi Madapusi | timeline score: 25 | |
| Jul 30, 2013 at 1:34 | comment | added | Keerthi Madapusi | I'm not sure exactly what you're looking for. But there is a description of the bigger GSpin group as a stabilizer of certain tensors in the first section of my paper here: math.harvard.edu/~keerthi/papers/reg.pdf | |
| Jul 29, 2013 at 17:07 | comment | added | user36938 | @shu: he wants ${\rm{Spin}}$ to be the group of all automorphisms, not merely to be a subgroup of an automorphism group. So the examples with $L^2$-functions don't fit that situation (e.g., for similar reasons, the fact that Spin groups are found inside Clifford algebras doesn't immediately furnish an answer when $n$ is not very small). | |
| Jul 29, 2013 at 16:00 | answer | added | Robert Bryant | timeline score: 17 | |
| Jul 29, 2013 at 15:22 | comment | added | shu | I always think $\mathrm{SO}(n)$ as 'automorphisms' of $L^2(\mathbb{R}^n)$, and $\mathrm{Spin}(n)$ as 'automorphisms' of $L^2(\mathbb{R}^n,S^{\mathbb{R}^n})$, where $S^{\mathbb{R}^n}$ is the spinor. | |
| Jul 29, 2013 at 14:45 | comment | added | Mikhail Borovoi | @JimHumphreys: tag added! | |
| Jul 29, 2013 at 14:26 | history | edited | Mikhail Borovoi |
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| Jul 29, 2013 at 13:57 | comment | added | Jim Humphreys | Maybe a tag 'lie-groups' would also be useful, since these groups arise naturally in Lie group theory. The differential geometric setting might offer a natural approach, though Spin groups are usually approached in any case via Clifford algebras. | |
| Jul 29, 2013 at 13:22 | comment | added | Mikhail Borovoi | Of course one can always say that $G$ is the automorphism group of the trivial torsor of $G$, but this is not the answer I am looking for. | |
| Jul 29, 2013 at 13:21 | history | asked | Mikhail Borovoi | CC BY-SA 3.0 |