The objective of the present paper is to report some progress on Ringel-Hall algebras of finite dimensional hereditary algebras and their relations with Kac-Moody algebras and quantum groups. Besides Ringel's work ([37]-[46]), the works of Green [11], Sevenhant-Van den Bergh [48, 49], and Frenkel-Malkin-Vybornov [9], as well as [51, 35, 52, 4, 5, 6], etc., are important for this survey. Of course, the topics covered naturally reflect the viewpoints and interests of the authors. We should stress that, due to lack of space and knowledge, we do not include many other important, topics related to Ringel's Hall algebra approach.
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机译：本文的目的是在有限维遗传代数的Ringel-Hall代数及其与Kac-Coody代数和量子群的关系中报告一些进展。除了菱格的作品外（[37] - [46]），绿色的作品[11]，Sevenhant-van den Bergh [48,49]和Frenkel-Malkin-Vybornov [9]，以及[51,35， 52,4,5,6]等对该调查很重要。当然，所涵盖的主题自然反映了作者的观点和利益。我们应该强调，由于缺乏空间和知识，我们不包括许多其他重要的主题，与菱形大厅代数方法相关。
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