English

Green formula in Hall algebras and cluster algebras

Representation Theory 2008-04-15 v1 Rings and Algebras

Abstract

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\bbc^{*}-action.

Cite

@article{arxiv.0804.2015,
  title  = {Green formula in Hall algebras and cluster algebras},
  author = {Jie Xiao and Fan Xu},
  journal= {arXiv preprint arXiv:0804.2015},
  year   = {2008}
}

Comments

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

R2 v1 2026-06-21T10:30:13.135Z