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After reading some threads I decided to post my question, since I couldn't find an sufficient answer.

In general the generators of a lie group combined with the compostion [A,B]=ifB build a Lie-Algebra. Where the Generators build the base of the vectorspace.

In a common vectorspace you can find a orthonormalbase, and the scalarproduct defines the metrik. How does the comutation relations fit in this concept? I know that the comutation relations show if two entities can be measured together with any accuracy, but what is their meaning referring to the understanding of a algebra?

I have the feeling I disorganised the whole concept...

In general the generators of a lie group combined with the compostion [A,B]=ifB build a Lie-Algebra. Where the Generators build the base of the vectorspace.

In a common vectorspace you can find a orthonormalbase, and the scalarproduct defines the metrik. How does the comutation relations fit in this concept? I know that the comutation relations show if two entities can be measured together with any accuracy, but what is their meaning referring to the understanding of a algebra?

I have the feeling I disorganised the whole concept...

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