Timeline for Computing centralizers of finite sets in right angled Artin groups (RAAGs) / partially commutative groups / graph groups
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 26, 2018 at 16:24 | comment | added | YCor | No, I can compute the centralizer in the linear representation (a certain subspace, actually subalgebra, of the matrix algebra), but you still have to determine the intersection of the subgroup with this given subspace, and as I said I don't even know it to be finitely generated and only expect it. | |
| Jun 26, 2018 at 16:12 | history | edited | Boaz Tsaban | CC BY-SA 4.0 |
added 110 characters in body
|
| Jun 26, 2018 at 16:09 | comment | added | Boaz Tsaban | @YCor thanks! Doesn't your answer imply there is a (cubic, say) algorithm for the problem? But perhaps pulling back to the RAAG may be difficult? (PS I am ashamed to say that I enjoyed many comments of yours thus far, and still do not know who you are. Would appreciate knowing, if I may.) | |
| Jun 26, 2018 at 15:59 | comment | added | YCor | "Computing" a centralizing is not a clearly defined concept: what output should we expect? Actually, we can indeed expect that arbitrary centralizers in RAAGs are finitely generated and hope, as an output, to get generators of the given centralizer. Note that in principle this doesn't say whether two given centralizer are equal! However, RAAGs being linear, we can compute the centralizers in the matrix algebra, and hence determine whether two given finite subsets have equal centralizers. | |
| Jun 26, 2018 at 15:51 | history | asked | Boaz Tsaban | CC BY-SA 4.0 |