Re: Gelfand, NCG

[Phung Ho Hai <phung@msri.org>]

Cha`o anh Ai' Vie^.t,

mo+'i che^ anh co' mo^.t ca^u ma` anh da~ bu+.c mi`nh thuye^'t cho mo^.t
ba`i da`i ro^`i. The^' mo+'i bie^'t bi. che^ kho' chi.u the^' na`o.
Any way, vie^.c anh ap dung NCG va`o va^.t ly' kho^ng co' nghi~a anh
hie^?u NCG mo^.t ca'ch toa'n ho.c. Thu+.c ra die^`u nay cha(?ng co' gi`
la.. Ca'c nha va^.t ly' invented tensor product song ra^'t nhie^`u nguo+.i
la`m va^.t ly' ly' thuye^'t kho^ng hie^?u duo.c kha'i nie^.n tensor
product trong toa'n ho.c.
Toi no'i anh "cuoi ngua xem hoa" vi` anh nha^`m la^~n giu+a hai di.nh ly'
cua? Gelfand va` Gelfand-Najmark khi noi ve^` NCG.

A` anh co`n ba('t be? hai ca'i thua^.t ngu+~ topo va` geometry. Topo la`
gi` ne^'u nhu+ kho^ng pha?i la` hi`nh ho.c. Nghie^n cu+'u hi`nh ho.c trong
toa'n kho^ng nha^'t thie^'t la` cu+' pha?i co' mo^.t toa'n tu+? De Rham.
Thua^.t ngu+~ geometry anh hie^?u trong toa'n go.i la` mo^.t differential
structure.

Ca'i triple ma` anh no'i de^'n co' the^? hie^?u la` "mo^.t kg topo
(non-comm), mo^.t diff. structure va` mo^.t phe'p ti'ch pha^n"
Ca'i da.i so^' A trong ca'i triple a^'y no' pha^n ba^.c va` tha`nh pha^`n
ba^.c 0 xa'c di.nh kg. topo (non-comm)-bo+?i do^'i nga^~u Gelfand.