The graded product of real spectral triples

Farnsworth, Shane

doi:10.1063/1.4975410

アイテム詳細

登録内容を編集ファイル形式で保存

一時保存へ追加

このアイテムの新しいバージョンが利用可能です:
https://pure.mpg.de/pubman/item/item_2428214_3

詳細要約

公開

学術論文

The graded product of real spectral triples

MPS-Authors

Farnsworth, Shane
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

External Resource

There are no locators available

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

フルテキスト (公開)

1605.07035.pdf
(プレプリント), 569KB

付随資料 (公開)

There is no public supplementary material available

引用

Farnsworth, S. (2017). The graded product of real spectral triples. Journal of Mathematical Physics, 58:. doi:10.1063/1.4975410.

引用: https://hdl.handle.net/11858/00-001M-0000-002D-238F-2

要旨

Forming the product of two geometric spaces is one of the most basic operations in geometry, but in the spectral-triple formulation of non-commutative geometry, the standard prescription for taking the product of two real spectral triples is problematic: among other drawbacks, it is non-commutative, non-associative, does not transform properly under unitaries, and often fails to define a proper spectral triple. In this paper, we explain that these various problems result from using the ungraded tensor product; by switching to the graded tensor product, we obtain a new prescription where all of the earlier problems are neatly resolved: in particular, the new product is commutative, associative, transforms correctly under unitaries, and always forms a well defined spectral triple.