Ringel-Hall Algebras Beyond their Quantum Groups I: Restriction Functor and Green Formula
Ringel-Hall Algebras Beyond their Quantum Groups I: Restriction Functor and Green Formula
复制标题
超越量子群的林格尔-霍尔代数 I：限制函子和绿色公式
DOI：
10.1007/s10468-018-9821-5
复制
发表时间：
2019
影响因子：
0.6
通讯作者：
Zhao Minghui
中科院分区：
文献类型：
--
作者：
Xiao Jie;Xu Fan;Zhao Minghui
本文将Lusztig引入的量子群及其标准基的代数结构推广到整个Ringel-Hall代数的一般形式。阐明了绿色公式与约束函子之间的显式关系。通过对绿色公式的几何证明，证明了在Lusztig框架下，Ringel-Hall代数的乘法与余乘法的相容性是可以分类的.
In this paper, we generalize the categorifical construction of a quantum group and its canonical basis introduced by Lusztig to the generic form of the whole Ringel-Hall algebra. We clarify the explicit relation between the Green formula and the restriction functor. By a geometric way to prove the Green formula, we show that the compatibility of multiplication and comultiplication of a Ringel-Hall algebra can be categorified under Lusztig’s framework.