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arXiv · 1312.6526

Left-symmetric algebroids

Jiefeng Liu·Yunhe Sheng·Chengming Bai·Zhiqi Chen
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Abstract

In this paper, we introduce a notion of a left-symmetric algebroid, which is a generalization of a left-symmetric algebra from a vector space to a vector bundle. The left multiplication gives rise to a representation of the corresponding sub-adjacent Lie algebroid. We construct left-symmetric algebroids from $\mathcal O$-operators on Lie algebroids. We study phase spaces of Lie algebroids in terms of left-symmetric algebroids. Representations of left-symmetric algebroids are studied in detail. At last, we study deformations of left-symmetric algebroids, which could be controlled by the second cohomology class in the deformation cohomology.

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Jiefeng Liu, Yunhe Sheng, Chengming Bai, Zhiqi Chen. 2013-12-23. Left-symmetric algebroids. https://doi.org/10.1002/mana.201300339

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