解生成技术的代数分类
An Algebraic Classification of Solution Generating Techniques
摘要：
我们考虑一个双重的问题：一方面，一个家庭的解决方案产生的技术（修改）超引力的分类，另一方面，一个家庭的规范变换的2维$σ$模型引起的可积保持变换的分类。假设一个广义Scherk-Schwarz模型，事实上，这两个问题承认基本上相同的代数公式，从一个潜在的双重李代数$\mathfrak d$出现。在介绍了我们的分类推导之后，我们详细讨论了与修正超引力的关系以及恢复标准（未修正）超引力的附加条件。从我们的主方程-编码所有可能的连续变形允许在家庭的解决方案生成技术-我们表明，这些分类的李代数上同调$H^2(\mathfrak h,\mathbb R)$和$H^3(\mathfrak h,\mathbb R)$的最大各向同性子代数$\mathfrak h$的双重李代数$\mathfrak d$。{We我们用一个非平凡的例子，bi-Yang-Escherter-Wess-Zumino模型来说明我们的结果。
英文摘要：
We consider a two-fold problem: on the one hand, the classification of a family of solution-generating techniques in (modified) supergravity and, on the other hand, the classification of a family of canonical transformations of 2-dimensional $σ$-models giving rise to integrable-preserving transformations. Assuming a generalised Scherk-Schwarz ansatz, in fact, the two problems admit essentially the same algebraic formulation, emerging from an underlying double Lie algebra $\mathfrak d$. After presenting our derivation of the classification, we discuss in detail the relation to modified supergravity and the additional conditions to recover the standard (unmodified) supergravity. Starting from our master equation - that encodes all the possible continuous deformations allowed in the family of solution-generating techniques - we show that these are classified by the Lie algebra cohomologies $H^2(\mathfrak h,\mathbb R)$ and $H^3(\mathfrak h,\mathbb R)$ of the maximally isotropic subalgebra $\mathfrak h$ of the double Lie algebra $\mathfrak d$. {We illustrate our results with a non-trivial example, the bi-Yang-Baxter-Wess-Zumino model.
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