The finite dual of commutative-by-finite Hopf algebras
| Autor: | Brown, Ken, Couto, Miguel, Jahn, Astrid |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | The finite dual $H^{\circ}$ of an affine commutative-by-finite Hopf algebra $H$ is studied. Such a Hopf algebra $H$ is an extension of an affine commutative Hopf algebra $A$ by a finite dimensional Hopf algebra $F$. The main theorem gives natural conditions under which $H^{\circ}$ decomposes as a crossed or smash product of $F^{\ast}$ by the finite dual of $A$. This decomposition is then further analysed using the Cartier- Gabriel-Kostant theorem to obtain component Hopf subalgebras of $H^{\circ}$ mapping onto the classical components of $A^{\circ}$. The detailed consequences for a number of families of examples are then studied. Comment: Preliminary version; comments welcome |
| Databáze: | arXiv |
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