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arXiv · 2510.19458

Foundations of Noncommutative Carrollian Geometry via Lie-Rinehart Pairs

Andrew James Bruce
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Abstract

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.

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BibTeXRIS

Andrew James Bruce. 2025-10-22. Foundations of Noncommutative Carrollian Geometry via Lie-Rinehart Pairs. https://doi.org/10.1088/1751-8121/ae454e

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