Jordan decomposition in an affine algebraic group
= Jordan decomposition in an affine algebraic group
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This is the multiplicative <Jordan–Chevalley decomposition> in a <linear algebraic group>. Every element $g$ of an affine algebraic group has unique commuting semisimple and unipotent parts $g_s,g_u$ such that $g=g_sg_u$. The construction agrees with the multiplicative <Jordan normal form>[Jordan decomposition] in every rational representation.