Projective real calculi over matrix algebras

In analogy with the geometric situation, we study real calculi over projective modules and show that they can be realized as projections of free real calculi. Moreover, we consider real calculi over matrix algebras and discuss several aspects of the classification problem for real calculi in this ca...

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Bibliographic Details
Published in:arXiv.org 2021-07
Main Author: Axel Tiger Norkvist
Format: Article
Language:English
Subjects:
Algebra
Calculi
Eigenvectors
Matrix representation
Modules
Online Access:Get full text
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Summary:In analogy with the geometric situation, we study real calculi over projective modules and show that they can be realized as projections of free real calculi. Moreover, we consider real calculi over matrix algebras and discuss several aspects of the classification problem for real calculi in this case, leading to the concept of quasi-equivalence of matrix representations. We also use matrix algebras to give concrete examples of real calculi where the module is projective, and show that the existence of a Levi-Civita connection depends on the eigenvectors of specific anti-hermitian matrices in this case.
ISSN:2331-8422