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== Generalizations == This rather evident construction may be extended in numerous and significant ways. For instance we may take any group homomorphism Ο from ''H'' to ''G'', instead of the [[inclusion map]], and define the restricted representation of ''H'' by the composition : <math> \rho\circ\varphi \, </math> We may also apply the idea to other categories in [[abstract algebra]]: [[associative algebra]]s, rings, [[Lie algebra]]s, [[Lie superalgebra]]s, Hopf algebras to name some. Representations or [[module (mathematics)|module]]s ''restrict'' to subobjects, or via homomorphisms.
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