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.

中文翻译：

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李代数的同调截面

我们研究了配备同调部分的李（超）代数，即“自交换”的奇数部分，我们将这种李代数称为内 Q-代数：这些提供了适当“超”Q-代数的自然例子梅塔的感觉。这样的李代数是 Q 流形和配备同调元素的李超代数的自然推广。在其他结果中，我们表明，通过派生的括号形式，内部 Q 代数的截面空间配备了一个奇 Loday-Leibniz 括号。