Antipode

The antipode , the last piece of a Hopf algebra: the unique map with .

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Antipode(element)

Domain: Hopf algebras

Details

• On a graded connected Hopf algebra the axiom DETERMINES : splitting off the two trivial terms of gives , and the left factor's degree strictly drops, so the recursion terminates
• Computed that way and then verified by running the axiom, rather than trusted
• On a commutative Hopf algebra is an involution, so on QSym

Examples

See also: Coproduct, QSymM