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DHSP TP. HCfuI
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Ee thi chinh thri'c
z )5,
I{oc phin : E4i so 4+ut 6a- A,u
kj 2. ndm hoc 2005 -2006
Hc-,c
4 0
Lcrp Cu nhdn vdt l1i
Tht:i gian: 6o phut
l:
Bai
Nhdn dang ciutmg bic hai sau: .ri -g.r,r, +7xl =g
Bai 2:
a) chirnu minh ky hi€u delta Kronecker d1 la mot renNo hon lrop hang 3.
b) Xdc clinh tenxo inetric trons roa d6 ciu.
Bai 3:
a) Trdn g: R3: (i =(1,0.0),i =(0.1.0),f =(0,0,1)) cho moc Lie
[...] la rich
co hucrng rhdng thucrng : k.fj,kf= i,[A,i]= 7. Chung ininh f
[t,i] = la rndt
d+i sd Lie 3-chidu.
b) Einh nghla bi€u di6n tuy6n tinh cua 1 nhorn. N€u I vi du vd
bieu di6n t*rng
thanh cira nh6m SO(2).
Bai 4:
a) Liet ke tdt ca cdc dai sO Lie thuc Z-chidu.
b) Cho / e L(3.R) la 6nh xa tuydn rinh ken R3 co ma rrdn
bi6u clien ln
f:ool
o=i' t Fliyxac dinh matrdn cta6nh xaexponenr cira/
u
l.
Ll I 2l
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