Infinitesimal ideal systems and the Atiyah class

Madeleine Jotz Lean

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arXiv · 1910.04492

Infinitesimal ideal systems and the Atiyah class

Madeleine Jotz Lean

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Abstract

This short note gives a geometric interpretation of the Atiyah class of a Lie pair. It proves that it vanishes if the subalgebroid is the kernel of a fibration of Lie algebroids. In other words, the Atiyah class of a Lie pair vanishes if the subalgebroid is the fiber of an ideal system in the Lie algebroid. In order to prove this, a new characterisation of the ideal condition for an infinitesimal ideal system is found.

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Madeleine Jotz Lean. 2019-10-10. Infinitesimal ideal systems and the Atiyah class. https://arxiv.org/abs/1910.04492

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