The number of generators of Lie algebra sl(2,C) is 6, and sl(2,R) has 3 generators, Can Lie algebra sl(2,C) be decomposed to direct sum of two sl(2,R)? Say sl(2,C)=sl(2,R)⊕sl(2,R) ?
If this holds, can you give one explicit representation of those generators?
By the way there is a similar relation which I know is hold so(4)=su(2)⊕su(2).
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