  We consider quantum symmetric algebras, FRT bialgebras and, more generally,
intertwining algebras for pairs of Hecke symmetries which represent quantum
hom-spaces. The paper makes an attempt to investigate Koszulness and
Gorensteinness of those graded algebras without a restriction on the parameter
q of the Hecke relation used earlier. When q is a root of 1, positive results
require a restriction on the indecomposable modules for the Hecke algebras of
type A that can occur as direct summands of representations in the tensor
powers of the base space.
