Abstract
The aim of the paper is to compute the global dimension of the algebras A in the title of the paper, their tensor products, some of their factor algebras. Some class of diskew polynomial rings belong to this class of algebras. Many classical algebras are examples of the algebras A (eg, U(sl(2)), U-q(sl(2)), the Heisenberg algebra and its quantum analogues, the Witten's deformations, the Woronowicz's deformation, O-q(SL2(K)) and others). As a consequence, the exact value of the global dimension is computed for well-known quantum algebras, their localizations and tensor products.