Equivalence of representations refers to the condition where two representations of a Lie algebra or Lie group are considered to be 'the same' in a certain sense. This typically involves finding a linear isomorphism between the vector spaces associated with these representations that intertwines the action of the Lie algebra or group, preserving the structure and relations inherent to those representations. Recognizing when two representations are equivalent is crucial for simplifying problems in representation theory, as it allows one to work with a single representative from each equivalence class.
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