Timeline for Lattice in a certain Lie group
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Dec 5, 2012 at 22:25 | comment | added | Misha | The proof that the group of upper triangular matrices $U_n$ is not unimodular could be found for instance in Bump's book "Automorphic forms and representations", page 426. | |
| Dec 5, 2012 at 17:05 | comment | added | Jim Humphreys |
To Misha's remarks I'd add the comment that Example 3 (on page 2 of the lecture notes he links from Tata) illustrates for $n=2$ why this type of solvable group isn't unimodular. I'm not sure how to sort out those solvable Lie groups which are unimodular, but an old theorem of Mostow shows that any lattice must then be arithmetic. (Venkatarama gives a few of the standard references.)
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| Dec 5, 2012 at 16:21 | vote | accept | Edward Cooper | ||
| Dec 5, 2012 at 5:16 | answer | added | Misha | timeline score: 14 | |
| Dec 5, 2012 at 5:08 | comment | added | Misha | See e.g. Corollary 1 on page 3 of Venkataramana's notes on lattices: math.lsu.edu/~pdani/conferences/goa2010/SpeakerNotes/… | |
| Dec 5, 2012 at 4:50 | comment | added | Edward Cooper | @Misha : Can you give me a reference for the fact that locally compact groups that contain lattices have to be unimodular? | |
| Dec 5, 2012 at 4:41 | comment | added | Misha | If a locally compact group $G$ contains a lattice, then $G$ has to be unimodular and you $G_n$ is not. | |
| Dec 5, 2012 at 4:03 | history | asked | Edward Cooper | CC BY-SA 3.0 |