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arXiv · 2010.13586

Homological sections of Lie algebroids

Andrew James Bruce
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Abstract

We examine Lie (super)algebroids equipped with a homological section, i.e., an odd section that `self-commutes', we refer to such Lie algebroids as inner Q-algebroids: these provide natural examples of suitably "superised" Q-algebroids in the sense of Mehta. Such Lie algebroids are a natural generalisation of Q-manifolds and Lie superalgebras equipped with a homological element. Amongst other results, we show that, via the derived bracket formalism, the space of sections of an inner Q-algebroid comes equipped with an odd Loday-Leibniz bracket.

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Andrew James Bruce. 2020-10-26. Homological sections of Lie algebroids. https://doi.org/10.1016/j.difgeo.2021.101826

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