= Absolute irreducibility of a group representation
= Absolute irreducibility
{synonym}
A <group representation> over a <field> is absolutely <irreducible> if it remains <irreducible> after every <field extension>. For a finite-dimensional <representation> it is enough to check an <algebraic closure>. Irreducibility over the original <field> alone is weaker: the two-dimensional real rotation <representation> of the cyclic group of order three splits into two lines over the complex numbers.
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