论文标题
狄拉克几何I：交换代数
Dirac geometry I: Commutative algebra
论文作者
论文摘要
光谱中的交换代数的同型组形成了分级阿贝尔基团的对称单体类别的交换代数。分级和Koszul符号规则是由Anima编码的结构的残余，而不是集合。本文及其续集的目的是开发从这种代数建造的几何形状。我们将这种几何形状命名，因为分级表现出旋转的标志。确实，它是由Anima编码的内部结构的反映，它像自旋一样区分了对称和反对称行为。此外，我们在续集中开发的连贯的共同体学承认了一半的serre曲折。
The homotopy groups of a commutative algebra in spectra form a commutative algebra in the symmetric monoidal category of graded abelian groups. The grading and the Koszul sign rule are remnants of the structure encoded by anima as opposed to sets. The purpose of this paper and its sequel is to develop the geometry built from such algebras. We name this geometry Dirac geometry, since the grading exhibits the hallmarks of spin. Indeed, it is a reflection of the internal structure encoded by anima, and it distinguishes symmetric and anti-symmetric behavior, as does spin. Moreover, the coherent cohomology, which we develop in the sequel admits half-integer Serre twists.
