The quantized enveloping algebra Uq is constructed as a quotient of the generalized quantum double U≤0 q τ U≥0 q associated to a natural skew pairing τ : U≤0 q ⊗ U≥0 q → k. This double is generalized by D = (B(V ) > F) τ (B(W) > G), where F, G are abelian groups, V ∈ FF YD, W ∈ GG YD are Yetter-Drinfeld modules and B(V ), B(W) are their Nichols algebras. We prove some results on Hopf ideals of D, including a characterization of what we call thin Hopf ideals. As an application we give an explicit description of those minimal quasitriangular pointed Hopf algebras in characteristic zero which are generated by skew primitives.
雑誌名
Journal of mathematical sciences, the University of Tokyo
巻
16
号
4
ページ
545 - 576
発行年
2010-03-25
ISSN
13405705
書誌レコードID
AA11021653
日本十進分類法
415
Mathematical Reviews Number
MR
Mathmatical Subject Classification
16W30(MSC2000)
17B37(MSC2000)
出版者
Graduate School of Mathematical Sciences, The University of Tokyo
On minimal quasitriangular pointed Hopf~ algebras
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