Global and Krull dimensions of quantum Weyl algebras

Given a Hecke symmetry R, A. Giaquinto and J. Zhang defined a natural quant ization A(n)(R) of the nth Weyl algebra A(n) based on R and studied many ri ng theoretic properties of rings A(2)(J(a,b)) (arising from the "Jordan" He cke symmetry) and A(n)(q, p(i,j)) (arising from the standard multiparameter Hecke symmetry). Here we compute the global and Krull dimensions in the ca ses that were left open; namely, we show that over any field k of character istic zero, gldim(A(2)(J(a,b))) = Kdim(A(2)(J(a,b))) = 3 for any a, b is an element of k with a not equal b, and gldim(A(n)(+/- 1, p(i,j))) = Kdim(A(n )(+/- 1, p(i,j))) = n. (C) 1999 Academic Press.