Homological Aspects of Noetherian PI Hopf Algebras and Irreducible Modules of Maximal Dimension
Homological Aspects of Noetherian PI Hopf Algebras and Irreducible Modules of Maximal Dimension
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DOI：
10.1006/jabr.1997.7109
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发表时间：
1997-12
影响因子：
0.9
通讯作者：
K. Brown;K. Goodearl
中科院分区：
文献类型：
--
作者：
K. Brown;K. Goodearl
Abstract 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.
