✦ LIBER ✦
Homological Aspects of Noetherian PI Hopf Algebras and Irreducible Modules of Maximal Dimension
✍ Scribed by K.A. Brown; K.R. Goodearl
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 314 KB
- Volume
- 198
- Category
- Article
- ISSN
- 0021-8693
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✦ Synopsis
We prove that a Noetherian Hopf algebra of finite global dimension possesses further attractive homological properties, at least when it satisfies a polynomial identity. This applies in particular to quantized enveloping algebras and to quantized function algebras at a root of unity, as well as to classical enveloping algebras in positive characteristic. In all three cases we show that these algebras are Auslander-regular and Macaulay. We derive representation theoretic consequences concerning the coincidence of the non-Azumaya and singular loci for each of the above three classes of algebras.