Abstract
AbstractThe 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.
Publisher
Cambridge University Press (CUP)