再论双场论中代数胚的双方面
More on Doubled Aspects of Algebroids in Double Field Theory
摘要：
我们继续研究双场论（DFT）中带有C-括号的代数体结构的二重化问题。我们发现，一个家庭的代数胚，Vaisman（度量或前DFT），前和前Courant代数胚的构造类似的Drinfel'd双李代数胚对。我们研究这些代数体的几何实现的仿厄米流形，这是一个实现的DFT中的双重时空。我们表明，在DFT中的强约束是必要的，以实现双重和非平凡的泊松结构，但可以放松一些代数体。简要讨论了扭括号的二重结构以及与群流形相关的二重结构。
英文摘要：
We continue to study doubled aspects of algebroid structures equipped with the C-bracket in double field theory (DFT). We find that a family of algebroids, the Vaisman (metric or pre-DFT), the pre- and the ante-Courant algebroids are constructed by the analogue of the Drinfel'd double of Lie algebroid pairs. We examine geometric implementations of these algebroids in the para-Hermitian manifold, which is a realization of the doubled space-time in DFT. We show that the strong constraint in DFT is necessary to realize the doubled and non-trivial Poisson structures but can be relaxed for some algebroids. The doubled structures of twisted brackets and those associated with group manifolds are briefly discussed.
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