Timeline for Which groups can occur as the group of units of finite-dimensional noncommutative algebras?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 8, 2017 at 10:48 | comment | added | Benjamin Steinberg | Im not sure if you can get any. | |
| Oct 8, 2017 at 9:52 | comment | added | M.G. | @BenjaminSteinberg: Thanks! If I understand you correctly, that means that the group of units is then recovered as a semidirect product of $\mathrm{GL}$-s and a connected unipotent group (and the latter is a closed subgroup of upper-triangular matrices). So, a natural question is then if any connected unipotent group can be realized (in the way you described above)? | |
| Oct 7, 2017 at 21:36 | comment | added | Benjamin Steinberg | If you factor the algebra by its radical you get a product of matrix algebras so the group of units has a connected unipotent normal subgroup such that the quotient is a product of general linear groups (unipotent since the radical is nilpotent, connected because it is a coset of the radical which is a linear space). Moreover, this quotient splits by the Wedderburn-Malcev theorem. | |
| Oct 7, 2017 at 14:39 | history | edited | M.G. |
added tag 'associative algebras'
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| Oct 7, 2017 at 14:34 | history | edited | Peter Heinig | CC BY-SA 3.0 |
Removed 'Thanks!'. Stylistic edits.
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| Oct 7, 2017 at 14:29 | history | edited | M.G. | CC BY-SA 3.0 |
forgot characteristic
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| Oct 7, 2017 at 14:24 | history | asked | M.G. | CC BY-SA 3.0 |