Module representation refers to the way in which a given algebraic structure, specifically a module over a ring, can be expressed through linear transformations acting on vector spaces. This concept is fundamental in understanding how different algebraic entities interact and how their symmetries can be represented using matrices or linear maps. In the context of Lie algebras, module representations provide insights into the action of the Lie algebra on various spaces, helping to uncover properties of the algebra itself and its representations.
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