CATENARITY IN QUANTUM ALGEBRAS

Various quantum algebras are shown to be catenary, i.e., all saturated chains of prime ideals between any two fixed primes have the same len gth. Further, Tauvel's formula relating the height of a prime ideal to the Gelfand-Kirillov dimension of the corresponding factor ring is es tablished. These results are obtained for coordinate rings of quantum affine spaces, for quantized Weyl algebras, and for coordinate rings o f complex quantum general linear groups, as well as for quantized enve loping algebras of maximal nilpotent subalgebras of semisimple complex Lie algebras.