Hall代数和簇代数中的Green公式
Green formula in Hall algebras and cluster algebras
摘要：
本文综述了近年来通过各种形式的格林公式将Ringel-Hall型代数方法应用于量子群和团簇代数的研究进展。本文着重介绍格林公式的三种形式：（1）格林公式的原始形式\cite{Green} \cite{RingelGreen}，（2）格林公式\cite{DXX}的退化形式，（3）格林公式\cite{XX2007a}的投影形式，即带有$\bbc^{*}$作用量的格林公式。
英文摘要：
The objective of the present paper is to give a survey of recent progress on applications of the approaches of Ringel-Hall type algebras to quantum groups and cluster algebras via various forms of Green's formula. In this paper, three forms of Green's formula are highlighted, (1) the original form of Green's formula \cite{Green}\cite{RingelGreen}, (2) the degeneration form of Green's formula \cite{DXX} and (3) the projective form of Green's formula \cite{XX2007a} i.e. Green formula with a $\bbc^{*}$-action.
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