Green formula in Hall algebras and cluster algebras

Details Green formula in Hall algebras and cluster algebras Green formula in Hall algebras and cluster algebras

2008-04-12

arxiv.org/abs/0804.2015v1

Mathematics

Representation Theory

The paper was published in the Proceedings of the 4th international congress of chinese mathematicians

Scientific paper

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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