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1.
The group of Hopf algebra automorphisms for a finite-dimensional semisimple cosemisimple Hopf algebra over a field k was considered by Radford and Waterhouse. In this paper, the groups of Hopf algebra automorphisms for two classes of pointed Hopf algebras are determined. Note that the Hopf algebras we consider are not semisimple Hopf algebras.   相似文献
2.
It is natural to define a Coxeter transformation in quantum groups by the product of Lusztig's symmetries in some order. In this note, we show that the Ringel–Hall algebra approach enables us to determine the behavior of its action in case of finite type.  相似文献
3.
Finite dimensional Hopf superalgebras u q (sl(m|n)) corresponding to the Lie superalgebras sl(m|n) are constructed. The PBW type basis and the left and right integrals of u q (sl(m|n)) are obtained. Furthermore, the group of Hopf superalgebra automorphisms is described.  相似文献
4.
It is shown that there exists a quantum superdeterminant sdet q T for the quantum super group OSP q (1|2n). It is also shown that the quantum superdeterminant sdet q T is a group-like element and central, and that the square of sdet q T for OSP q (1|2n) is equal to 1.  相似文献
5.
Let (Γ,I) be the bound quiver of a cyclic quiver whose vertices correspond to the Abelian group Zd. In this paper, we list all indecomposable representations of (Γ,I) and give the conditions that those representations of them can be extended to representations of deformed preprojective algebra Πλ(Γ,I). It is shown that those representations given by extending indecomposable representations of (Γ,I) are all simple representations of Πλ(Γ,I). Therefore, it is concluded that all simple representa-tions of rest...  相似文献
6.
The Gr?bner-Shirshov basis of the degenerate Ringel-Hall Algebras of type C3 is obtained by studying the generic extension monoid algebra.  相似文献
7.
设${\mathbb F}$是特征为零的代数闭域, $H$为非点化非幺模的8维非半单Hopf代数, $M_{2}({\mathbb F})$为${\mathbb F}$上二阶方阵组成的全矩阵代数. 本文的主要目的是讨论和分类$M_{2}({\mathbb F})$上所有的$H$-模代数结构.  相似文献
8.
本文我们定义复数域$C$上一般线性李代数${\rm gl}_n$ BGG 范畴的若干子范畴及其上的投射函子,利用这些子范畴和投射函子范畴化了$D_4$型李代数包络代数旋模的$n$-次张量积.  相似文献
9.
The aim of this paper is to categorify the n-th tensor power of the vector representation of U (so(7, C)). The main tools are certain singular blocks and projective functors of the BGG category of the complex Lie algebra gl n .  相似文献
10.
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