AR quivers, exceptional sequences and algorithms in derived Hall algebras
AR quivers, exceptional sequences and algorithms in derived Hall algebras
复制标题
DOI：
10.1007/s11425-010-3069-9
复制
发表时间：
2010-04
影响因子：
1.4
通讯作者：
Sheng Jie
中科院分区：
文献类型：
--
作者：
Sheng Jie
考虑量子群Uq（g）的正部U+与Hall代数H（Λ）之间的正则同构，其中半单李代数g和有限维遗传代数Λ共享一个Dynkin图。Chen和Xiao给出了两个算法，分别由Λ-模的例外序列上的辫群作用和Λ的Auslander-Reiten群的结构导出，将U ~+的Chevalley生成元的根向量分解为单项式的线性组合.本文给出了Toën引入的导出Hall代数DH（Λ）的相应算法.我们表明，这两种算法都适用于格代数和海森堡双重意义下的Kapranov。所有新的递推公式都与量子Serre关系具有相同的性质。
Consider the canonical isomorphism between the positive partU+of the quantum groupUq(g) and the Hall algebraH(Λ), where the semisimple Lie algebra g and the finite-dimensional hereditary algebra Λ share a Dynkin diagram. Chen and Xiao have given two algorithms to decompose the root vectors into linear combinations of monomials of Chevalley generators ofU+, respectively induced by the braid group action on the exceptional sequences of Λ-modules and the structure of the Auslander-Reiten quiver of Λ. In this paper, we obtain the corresponding algorithms for the derived Hall algebraDH(Λ), which was introduced by Toën. We show that both algorithms are applicable to the lattice algebra and Heisenberg double in the sense of Kapranov. All the new recursive formulae have the same flavor with the quantum Serre relations.