q-algebras and arrangements of hyperplanes

Varchenkoʹs approach to quantum groups, from the theory of arrangements of hyperplanes, can be usefully applied to q-algebras in general, of which quantum groups and quantum (super) Kac–Moody algebras are special cases. New results are obtained on the classification of q-algebras, and of the Serre ideals of generalized quantum (super) Kac–Moody algebras.