Linear connections on matrix geometries
J. Madore, T. Masson, J. Mourad
TL;DR
This paper discusses a new approach to defining linear connections in noncommutative geometry, providing examples based on matrix algebras that have unique metric connections.
Contribution
It introduces a general definition of linear connections in noncommutative geometry and presents specific examples with unique metric connections.
Findings
Examples of linear connections on matrix geometries
Existence of unique metric connections in these examples
Advancement in noncommutative geometric frameworks
Abstract
A general definition of a linear connection in noncommutative geometry has been recently proposed. Two examples are given of linear connections in noncommutative geometries which are based on matrix algebras. They both possess a unique metric connection.
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