HOMOLOGICAL ASPECTS OF NOETHERIAN PI HOPF-ALGEBRAS AND IRREDUCIBLE MODULES OF MAXIMAL DIMENSION

We prove that a Noetherian Hopf algebra of finite global dimension pos sesses further attractive homological properties, at least when it sat isfies a polynomial identity. This applies in particular to quantized enveloping algebras and to quantized function algebras at a root of un ity, as well as to classical enveloping algebras in positive character istic. In all three cases we show that these algebras are Auslander-re gular and Macaulay. We derive representation theoretic consequences co ncerning the coincidence of the non-Azumaya and singular loci for each of the above three classes of algebras. (C) 1997 Academic Press.