Some aspects of noncommutative differential geometry
Michel Dubois-Violette
TL;DR
This paper explores key aspects of noncommutative differential geometry, including reality conditions, differential calculi, derivation-based calculus, and connections, with applications to quantum mechanics.
Contribution
It introduces a general theory of connections within noncommutative differential geometry and relates derivation-based calculus to quantum mechanics.
Findings
Relations between derivation-based calculus and quantum mechanics
Formulation of a general theory of connections in noncommutative geometry
Discussion of reality conditions and differential calculi
Abstract
We discuss in some generality aspects of noncommutative differential geometry associated with reality conditions and with differential calculi. We then describe the differential calculus based on derivations as generalization of vector fields, and we show its relations with quantum mechanics. Finally we formulate a general theory of connections in this framework.
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Taxonomy
TopicsNoncommutative and Quantum Gravity Theories · Homotopy and Cohomology in Algebraic Topology · Advanced Operator Algebra Research