正则代数背景下代数与几何的相互作用
The Interplay of Algebra and Geometry in the Setting of Regular Algebras
摘要：
本文基于作者在MSRI的“女性联系”研讨会上于2013年1月发表的演讲，同时也是MSRI“非交换代数几何和表示论“项目的一部分。阐述的目的之一是激发和描述的几何技术介绍了M。Artin，J. Tate和M.范登伯格在20世纪80年代在一个水平接近研究生。此外，自20世纪90年代初以来，在这个问题上的一些进展进行了讨论，包括最近推广的完全交的非交换设置，和分次斜Clifford代数的概念和它的应用分类的二次正则代数的整体维数最多为3。文章最后列举了一些有待解决的问题。
英文摘要：
This article is based on a talk given by the author at MSRI in the workshop "Connections for Women" in January 2013, while being a part of the program "Noncommutative Algebraic Geometry and Representation Theory" at MSRI. One purpose of the exposition is to motivate and describe the geometric techniques introduced by M. Artin, J. Tate and M. Van den Bergh in the 1980s at a level accessible to graduate students. Additionally, some advances in the subject since the early 1990s are discussed, including a recent generalization of complete intersection to the noncommutative setting, and the notion of graded skew Clifford algebra and its application to classifying quadratic regular algebras of global dimension at most three. The article concludes by listing some open problems.
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