关于倾斜模和倾斜代数的几点注记。起源本案无关未来(An倾斜理论手册附录）
Some Remarks Concerning Tilting Modules and Tilted Algebras. Origin. Relevance. Future. (An appendix to the Handbook of Tilting Theory)
摘要：
这是即将出版的《倾斜理论手册》的附录，由安杰莱里-休格尔、哈佩尔和克劳斯编辑。附录的第一部分提供了倾斜理论核心的概要。第2部分是专门的主题，倾斜模块和倾斜代数已被证明是相关的。第1和第2部分都包含历史注释和回忆。最后的第3部分是一个简短的报告，对一些引人注目的最近的发展是由集群理论的福明和Zelevinsky的动机。特别是，我们将引导读者的基本性质集群倾斜代数，倾斜代数和集群倾斜代数之间的关系，而且集群类别提供了一个普遍的设置，所有相关的倾斜和集群倾斜代数。此外，我们将把注意力集中到集群倾斜对象的复杂性，并表现出这种复杂性的初步描述。
英文摘要：
This is an appendix to the Handbook of Tilting Theory, edited by Angeleri-Huegel, Happel and Krause, to be published soon. Part 1 of the appendix provides an outline of the core of tilting theory. Part 2 is devoted to topics where tilting modules and tilted algebras have shown to be relevant. Both Parts 1 and 2 contain historical annodations and reminiscences. The final Part 3 is a short report on some striking recent developments which are motivated by the cluster theory of Fomin and Zelevinsky. In particular, we will guide the reader to the basic properties of cluster tilted algebras, to the relationship between tilted algebras and cluster tilted algebras, but also to the cluster categories which provide a universal setting for all the related tilted and cluster tilted algebras. In addition, we will focus the attention to the complex of cluster tilting objects and exhibit an elementary description of this complex.
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