Homological sections of Lie algebroids |
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Institution: | Department of Mathematics, University of Luxembourg, Maison du Nombre 6, avenue de la Fonte, L-4364 Esch-sur-Alzette, Luxembourg |
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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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Keywords: | Q-manifolds Lie algebroids Derived brackets Loday–Leibniz algebras |
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