This article is based on a talk given by the author at the 12th International Conference on Clifford Algebras and their Applications in Mathematical Physics. A generalization, introduced by Cassidy and the author, of a classical Clifford algebra is discussed together with connections between that generalization and a generalization of a graded Clifford algebra. A geometric approach to studying the algebras, viewed through the lens of Artin, Tate and Van den Bergh’s noncommutative algebraic geometry, is also presented.

中文翻译：

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推广经典 Clifford 代数、分级 Clifford 代数及其相关几何

本文基于作者在第12 届克利福德代数及其在数学物理中的应用国际会议上的演讲。由 Cassidy 和作者介绍的经典 Clifford 代数的推广以及该推广与分级 Clifford 代数的推广之间的联系一起讨论。还介绍了一种研究代数的几何方法，通过 Artin、Tate 和 Van den Bergh 的非交换代数几何的视角进行观察。