  This paper improves several previously known results. First, the results
describing the R-skewsymmetric algebra and the quadratic dual of the
R-symmetric algebra as Frobenius algebras are shown to be true with any
restriction on the parameter q of the Hecke relation being removed. An even
Hecke symmetry gives rise to a pair of graded Frobenius algebras. We describe
interrelation between the Nakayama automorphisms of the two algebras. As an
illustration of general technique we give full details of the verification that
Artin-Schelter regular algebras of global dimension 3 and elliptic type A are
not associated with any quantum GL(3).
