  By finite quantum groups we mean Lusztig's finite-dimensional pointed Hopf
algebras called quantum Frobenius Kernels [9, 10], and their natural
generalizations due to Andruskiewitsch and Schneider [2, 3]. For a Hopf algebra
$H$ in a special class of the latter generalizations, which arises from a pair
of quantum linear spaces, Krop and Radford [8] described the simple modules
over $H$ and over the Drinfel'd double $D(H)$, showing that they fall into a
simple pattern of parametrization. We extend the description to a wider class
of Hopf algebras which includes the quantum Frobenius Kernels, renewing the
parametrization pattern so as to connect directly to the so-called triangular
decomposition.
