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As is well known, using the Hilbert Nullstellensatz (and a more recent result of Cartier) one can show that commutative finitely generated Hopf algebras over $\mathbb{C}$ are equivalent to algebraic groups (cf the accepted answeranswer of David Speyer). What happens when one considers finitely generated Hopf $*$-algebras? Does there exist an analogous equivalence with the star coming (perhaps) from matrix adjoints?

As is well known, using the Hilbert Nullstellensatz (and a more recent result of Cartier) one can show that commutative finitely generated Hopf algebras over $\mathbb{C}$ are equivalent to algebraic groups (cf the accepted answer of David Speyer). What happens when one considers finitely generated Hopf $*$-algebras? Does there exist an analogous equivalence with the star coming (perhaps) from matrix adjoints?

As is well known, using the Hilbert Nullstellensatz (and a more recent result of Cartier) one can show that commutative finitely generated Hopf algebras over $\mathbb{C}$ are equivalent to algebraic groups (cf the accepted answer of David Speyer). What happens when one considers finitely generated Hopf $*$-algebras? Does there exist an analogous equivalence with the star coming (perhaps) from matrix adjoints?

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Hans gluckmann
Hans gluckmann
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Finitely Generated Commutative Hopf $*$-Algebras

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Hans gluckmann
Hans gluckmann
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Commutative Hopf $*$-Algebras

As is well known, using the Hilbert Nullstellensatz (and a more recent result of Cartier) one can show that commutative finitely generated Hopf algebras over $\mathbb{C}$ are equivalent to algebraic groups (cf the accepted answer of David Speyer). What happens when one considers finitely generated Hopf $*$-algebras? Does there exist an analogous equivalence with the star coming (perhaps) from matrix adjoints?