Weight space
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Let V be a representation of a Lie algebra 
and assume that a Cartan subalgebra 
of is chosen. A weight space 
of weight 
is defined by
Similarly, we can define a weight space Vμ for representation of a Lie group resp. an associative algebra as the subspace of eigenvectors of some maximal commutative subgroup resp. subalgebra of the eigenvalue μ.
Elements of the weight spaces are called weight vectors.
