347 research outputs found
Left-symmetric algebroids
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 -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.Comment: 21 page
Rota-Baxter operators on Witt and Virasoro algebras
The homogeneous Rota-Baxter operators on the Witt and Virasoro algebras are
classified. As applications, the induced solutions of the classical Yang-Baxter
equation and the induced pre-Lie and PostLie algebra structures are obtained.Comment: 28 page
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