Noncommutative Geometry
In the context of Lie algebras, a weight space is a subspace associated with a specific weight in the representation theory of Lie algebras. Each weight corresponds to an eigenvalue of a Cartan subalgebra, and weight spaces are crucial for understanding the structure of representations, as they help categorize vectors according to their transformation properties under the action of the algebra. Weight spaces facilitate the decomposition of representations into simpler components, revealing the underlying symmetries and relationships within the algebra.
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