TL;DR
This paper introduces H-twisted Lie algebroids, a new algebraic structure satisfying a twisted Jacobi identity, with applications in classifying PQ3-manifolds through cohomology theories.
Contribution
It defines H-twisted Lie algebroids, explores their properties, and develops associated cohomology theories, advancing the understanding of twisted algebraic structures.
Findings
Defined H-twisted Lie algebroids with a closed 3-form twist.
Established three types of cohomology for these structures.
Classified PQ3-manifolds using the developed cohomology theories.
Abstract
We define a new kind of algebroid which fulfills a Leibniz rule, a Jacobi identity twisted by a 3-form with values in the kernel of the anchor map, and the twist is closed under a naturally occurring exterior covariant derivative. We give examples and define three kinds of cohomology two via realization as Q-structure on graded manifolds. This classifies PQ3-manifolds.
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