Timeline for Homomorphic Commutator? Equation
Current License: CC BY-SA 3.0
6 events
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| Oct 26, 2015 at 6:32 | history | edited | Sidharth Ghoshal | CC BY-SA 3.0 |
added 673 characters in body
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| Sep 18, 2015 at 6:53 | comment | added | მამუკა ჯიბლაძე | Something like this occurs in what B. Pachuashvili nicknamed "grgr=ab" :D I mean, category of internal groups in the category of groups is equivalent to the category of abelian groups (more generally, monoids would do). In other words, if you have a monoid $M$ and a second monoid structure on $M$ such that operations for the second structure are homomorphisms with respect to the first structure, then these structures actually coincide and are commutative. In the argument your equation appears, but units are essential. I don't know what one gets without them. | |
| Sep 17, 2015 at 20:48 | comment | added | Gerhard Paseman | Quite possible, in which case my reference won't help. However, more general notions of commutation (including the one you are using) have been studied in the context of general algebra. I am not willing at present to answer general questions, but if you think something I've suggested might help and have a specific point to resolve, I can probably help. Good Luck. Gerhard "Longest Commute Was Four States" Paseman, 2015.09.17 | |
| Sep 17, 2015 at 20:45 | comment | added | Sidharth Ghoshal | I believe I may be abusing the term "commutator" as I used it in a casual context, to indicate that my functional equation involved commuting or moving around arguments. | |
| Sep 17, 2015 at 20:44 | comment | added | Gerhard Paseman | If you need to come at this from a functional analysis point, I can't help. If you don't mind a general algebraic approach, there is a notion of commutator for general algebras. Freese, Kiss, and McKenzie are some authors that come to mind. If you come back with a question related to this question and concerning a point in commutator theory, I might be able to provide a hint. Gerhard "Then Again, I Might Not" Paseman, 2015.09.17 | |
| Sep 17, 2015 at 19:48 | history | asked | Sidharth Ghoshal | CC BY-SA 3.0 |