Timeline for Calculating the centralizer of a subgroup of $\mathrm{GL}(n, \mathbb{Z})$
Current License: CC BY-SA 4.0
7 events
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| Jun 2, 2023 at 13:45 | vote | accept | Jim | ||
| Jun 2, 2023 at 13:39 | comment | added | Jim | @YCor The input should be the generators $G_i$ and the output the generators of the centralizer. That the output is a complete should be verifiable. To find the generators by enumeration I came across this: semanticscholar.org/paper/… . But I don't think he proves the set is complete. | |
| Jun 2, 2023 at 13:01 | comment | added | YCor | You say "calculate the centralizer", but part of the question requires to specify what kind of input is expected. Actually, it follows from Borel–Harish-Chandra that the centralizer is finitely generated. Hence a possible output is a finite generating subset of the centralizer. (One could ask, as an output, to just enumerate the centralizer, but this is kind of trivial and mostly useless — namely one enumerates the centralizer in the rational (or integral) matrix algebra and then checks when one gets an element of $\mathrm{GL}_n(\mathbf{Z})$.) | |
| Jun 2, 2023 at 7:36 | answer | added | Derek Holt | timeline score: 9 | |
| Jun 2, 2023 at 6:59 | history | edited | YCor |
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| Jun 2, 2023 at 6:34 | history | edited | YCor | CC BY-SA 4.0 |
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| Jun 2, 2023 at 5:22 | history | asked | Jim | CC BY-SA 4.0 |