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Foundations of Noncommutative Carrollian Geometry via Lie-Rinehart Pairs
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Foundations of Noncommutative Carrollian Geometry via Lie-Rinehart Pairs
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Paper
Foundations of Noncommutative Carrollian Geometry via Lie-Rinehart Pairs
2026
Overview
Carrollian manifolds offer an intrinsic geometric framework for the physics in the ultra-relativistic limit. The recently introduced Carrollian Lie algebroids are generalised to the setting of \\(\\rho\\)-commutative geometry, (also known as almost commutative geometry), where the underlying algebras commute up to a numerical factor. Via \\(\\rho\\)-Lie-Rinehart pairs, it is shown that the foundational tenets of Carrollian geometry have analogous statements in the almost commutative world. We explicitly build two toy examples: we equip the extended quantum plane and the noncommutative \\(2\\)-torus with Carrollian structures. This opens up the rigorous study of noncommutative Carrollian geometry via almost commutative geometry.
Publisher
Cornell University Library, arXiv.org
Subject
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