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traceless matricies. The space of these matricies is 6-dimensional vector space

over real numbers field but is 3-dimensional space over complex numbers field.

Number of different representations of this algebra depend on how we look at

this algebra. If we assume that it's over complex number then it's just complexification

of [tex] \mathfrak{su}(2) [/tex] (all representation might be indexed by one integer or

halfinteger number). However if we treat it as space over real numbers then its

representation are index by pair of (half)integer numbers.