有限整体维数的有限维代数的加法不变量
Additive invariants of finite dimensional algebras of finite global dimension
摘要：
设k是一个完满域，A是一个有限维k-代数，其整体维数是有限的（例如，一个没有定向圈的有限域的路代数）.利用最近的非交换模理论，我们证明了在A处的每个加法不变量的值仅取决于单模的个数。添加剂不变量的例子包括代数K理论，循环同调（及其所有变种），拓扑霍赫希尔德同调等，一路上，我们建立两个结果的普遍兴趣。第一个问题是关于每一个真dg范畴的Grothendieck群上的双线性对与Galois作用之间的相容性。第二种是在非交换动机的设置下的迁移结果。
英文摘要：
Let k be a perfect field and A a finite dimensional k-algebra of finite global dimension (e.g. the path algebra of a finite quiver without oriented cycles). Making use of the recent theory of noncommutative motives, we prove that the value of every additive invariant at A only depends on the number of simple modules. Examples of additive invariants include algebraic K-theory, cyclic homology (and all its variants), topological Hochschild homology, etc. Along the way we establish two results of general interest. The first one concerns the compatibility between bilinear pairings and Galois actions on the Grothendieck group of every proper dg category. The second one is a transfer result in the setting of noncommutative motives.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
