$Q$-manifolds and Higher Analogs of Lie Algebroids

TL;DR

This paper explores the extension of the relationship between Q-manifolds and Lie algebroids to higher and non-linear analogs, introducing new algebraic structures that generalize Lie superalgebras.

Contribution

It introduces a new algebraic framework for higher analogs of Lie algebroids and generalizes Lie superalgebras using Q-manifolds.

Findings

Identifies identities satisfied by the new algebraic structures

Extends the relation between Q-manifolds and Lie algebroids to higher cases

Generalizes Lie superalgebras for point bases

Abstract

We show how the relation between $Q$-manifolds and Lie algebroids extends to ``higher'' or ``non-linear'' analogs of Lie algebroids. We study the identities satisfied by a new algebraic structure that arises as a replacement of operations on sections of a Lie algebroid. When the base is a point, we obtain a generalization of Lie superalgebras.