User talk:Miguel/Mathematics
From Wikipedia, the free encyclopedia
Hi Miguel, thanks a lot for your edits in the Math area! I hope you enjoy it as much as the rest of us.
In one of your subject lines, you mentioned that we should merge topological group and Lie group. I disagree: the concept of topological group is more general (they don't have to be manifolds, so for instance the Lp spaces are topological groups but not Lie groups), and the techniques in the two fields are very different (the whole machinery of Lie algebras is not available for topological groups). Also, between topological groups the natural morphisms are continuous group homomorphisms, while between Lie groups the natural morphisms are analytical group homomorphisms. AxelBoldt
Point taken. However, the example of Lp spaces is not really that good, because (with the operation of addition) it is not only an abelian group, but a vector space! In fact, you can use exploit the analogy with finite-dimensional spaces to develop a theory of "manifolds modelled on banach spaces".
A nonabelian infinite-dimensional topological group might be the group of diffeomorphisms of a manifold, but that does have a Lie algebra: the Lie algebra of complete vector fields. This is, in fact, one of the motivations for a theory of manifolds modelled on topological vector spaces.
This suggests to me that the reason Lp spaces don't appear to have lie algebras is that they are abelian, and therefore, the lie algebra is trivial. -- Miguel
By the way, it's cool how you guys pay attention to who comes in and what they do. -- Miguel
Yer a bum, Miguel!!! -- Toby Bartels
(And Axel: He admitted to me today that you were right.)
Hello. I have now added a clarification and illustration of the statement you considered dubious in the Archimedes article.
You did a very good job of listing his works. Michael Hardy 19:50 8 Jul 2003 (UTC)
He añadido unas cuantas cosas a tu artículo sobre Mathematical beauty. Espero que esto les valga a los Torquemada de la wikipedia para no borrarla. Supongo que habrá unos cuantos errores ortográficos y de estilo, pero espero que estés más o menos de acuerdo en lo esencial. Saludos Jmartinezot 10:08, 20 Aug 2003 (UTC)
Hi Miguel. Good work on mathematical beauty and mathematical fetishism issue - suggest a foundation of measurement article including the latter issue?
Hello, I just answered a question of yours on Talk:Sheaf. Cheers, AxelBoldt 15:42, 22 Nov 2003 (UTC)
Hi Miguel. Would you please look at "Talk:Black hole electron". There under, Matter-wave quantum, is the expression h = 2mc(3Gm)exponent 1/3, times (2pi)exponent 5/3. This may be only approximately correct but I believe it may be precisely correct. If you have an opinion about this, would you please let me know?--DonJStevens 17:08, 7 September 2007 (UTC)
