The finite dual of commutative-by-finite Hopf algebras
Glasgow mathematical journal, Tome 65 (2023) no. 1, pp. 62-89
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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 $\overline{H}$. The main theorem gives natural conditions under which $H^{\circ}$ decomposes as a crossed or smash product of $\overline{H}^{\ast}$ by the finite dual $A^{\circ}$ 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.
Brown, K. A.; Couto, M.; Jahn, A. The finite dual of commutative-by-finite Hopf algebras. Glasgow mathematical journal, Tome 65 (2023) no. 1, pp. 62-89. doi: 10.1017/S0017089522000052
@article{10_1017_S0017089522000052,
author = {Brown, K. A. and Couto, M. and Jahn, A.},
title = {The finite dual of commutative-by-finite {Hopf} algebras},
journal = {Glasgow mathematical journal},
pages = {62--89},
year = {2023},
volume = {65},
number = {1},
doi = {10.1017/S0017089522000052},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089522000052/}
}
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%0 Journal Article %A Brown, K. A. %A Couto, M. %A Jahn, A. %T The finite dual of commutative-by-finite Hopf algebras %J Glasgow mathematical journal %D 2023 %P 62-89 %V 65 %N 1 %U http://geodesic.mathdoc.fr/articles/10.1017/S0017089522000052/ %R 10.1017/S0017089522000052 %F 10_1017_S0017089522000052
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