The ramification of centres: Lie algebras in positive characteristic and quantised enveloping algebras
The ramification of centres: Lie algebras in positive characteristic and quantised enveloping algebras
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DOI：
10.1007/s002090100274
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发表时间：
1999-11
影响因子：
0.8
通讯作者：
K. Brown;I. Gordon
中科院分区：
文献类型：
--
作者：
K. Brown;I. Gordon
LetHbe a Hopf algebra over the fieldkwhich is a finite module over a central affine sub-Hopf algebraR. Examples include enveloping algebrasof finite dimensionalk-Lie algebrasin positive characteristic and quantised enveloping algebras and quantised function algebras at roots of unity. The ramification behaviour of the maximal ideals ofZ(H) with respect to the subalgebraRis studied, and the conclusions are then applied to the cases of classical and quantised enveloping algebras. In the case offorsemisimple a conjecture of Humphreys [28] on the block structure ofis confirmed. In the case offorsemisimple andan odd root of unity we obtain a quantum analogue of a result of Mirković and Rumynin, [35], and we fully describe the factor algebras lying over the regular sheet, [9]. The blocks ofare determined, and a necessary condition (which may also be sufficient) for a baby Verma-module to be simple is obtained.
