Timeline for Is $PSL(n, Z)$ isomorphic to a subgroup of $GL(n,C)$ or even $GL(n+1,C)$?
Current License: CC BY-SA 3.0
7 events
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| Apr 26, 2011 at 1:25 | comment | added | Tom Goodwillie | I think you can use a subgroup of $PSL(4,\mathbb Z)$ that is conjugate in $PSL(4,\mathbb R)$ to a subgroup of $PSO(4)\cong SO(3)\times SO(3)$ that is isomorphic to $A_4\times A_4$. | |
| Apr 25, 2011 at 15:25 | comment | added | Jim Humphreys |
This is definitely a creative approach, though I still wonder whether something more conceptual (in a more general context of arithmetic groups) is possible. Also, I wonder what an efficient subgroup choice would be for $n=4$?
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| Apr 25, 2011 at 15:21 | comment | added | Jim Humphreys | Rather than add this as an answer it would be preferable just to accept Tom's answer. | |
| Apr 25, 2011 at 1:51 | history | edited | Tom Goodwillie | CC BY-SA 3.0 |
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| Apr 24, 2011 at 18:23 | history | edited | Tom Goodwillie | CC BY-SA 3.0 |
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| Apr 24, 2011 at 15:39 | comment | added | John Franks | Thanks Tom. I was, of course, only interested in the n even case. Your answer definitively answers the question for my purposes. | |
| Apr 24, 2011 at 13:03 | history | answered | Tom Goodwillie | CC BY-SA 3.0 |