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From: ganesh on 8 Dec 2009 23:17
SU(2)xSU(2) has the same lie algebra as SO(4).
SU(2)xSU(2) is reducible into a 3 dimensional and 1 dimensional representation using say clebsh gordon coefficients. Does this imply that SO(4) is also reducible?

ganesh
From: José Carlos Santos on 9 Dec 2009 13:04
On 09-12-2009 14:17, ganesh wrote:

> SU(2)xSU(2) has the same lie algebra as SO(4).

Indeed.

> SU(2)xSU(2) is reducible into a 3 dimensional and 1 dimensional
> representation using say clebsh gordon coefficients. Does this
> imply that SO(4) is also reducible?

The term "reducible" applies group representations, not to the groups
themselves. Are you thinking about simple Lie groups?

Best regards,

Jose Carlos Santos
From: ganesh on 9 Dec 2009 22:56
I was thinking about the fundamental matrix representation actually. Let s1, s2, s3 be the generators which are 2x2 matrixes. Then exp(i.c1.s1 + i.c2.s2 + i.c3.s3) = U be a representation of SU(2), where c1,c2 & c3 are c-numbers.

Then UxU = 4x4 matrix -> is reducible to a 3 dim and 1 dim irreducible representations.

Similarly S0(4) can be represented by a 4x4 matrix (resultant of summing and exponentiating 6 generators).
Can this be reduced to a 3 dim and 1 dim irreducible representations?
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