The ramification of centres: Lie algebras in positive characteristic and quantised enveloping algebras

Details 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

1999-11-29

arxiv.org/abs/math/9911234v1

Mathematics

Representation Theory

42 pages, 1 table

Scientific paper

Let H be a Hopf algebra which is a finite module over a central sub-Hopf algebra R. The ramification behaviour of the maximal ideals of Z(H) with respect to the subalgebra R is studied. In the case when H is U(g), the enveloping algebra of a semisimple Lie algebra g, a conjecture of Humphreys is confirmed. In the case when H is the quantised enveloping algebra of g at a root of unity we obtain quantum analogues of result of a Mirkovic and Rumynin, we fully describe the reduced factor algebras over the regular sheet and the blocks of H are determined.

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