用扩展Maurer Cartan型生成高阶李代数
Generating Higher-Order Lie Algebras by Expanding Maurer Cartan Forms
摘要：
通过推广Maurer-Cartan展开法，构造了一个得到扩展高阶李代数的方法。得到了$\mathcal{G}=V_{0}\oplus V_{1}$情形下的高阶扩展Maurer-Cartan方程，并给出了S-扩展多重代数过程的对偶形式.通过选择一个特殊的半群，从S-展开形式恢复了扩展的高阶Maurer-Cartan方程.这种对偶方法可以用于找到对广义自由微分代数的情况的推广，这可能与物理应用有关，例如，高自旋规范理论。
英文摘要：
By means of a generalization of the Maurer-Cartan expansion method we construct a procedure to obtain expanded higher-order Lie algebras. The expanded higher order Maurer-Cartan equations for the case $\mathcal{G}=V_{0}\oplus V_{1}$ are found. A dual formulation for the S-expansion multialgebra procedure is also considered. The expanded higher order Maurer Cartan equations are recovered from S-expansion formalism by choosing a special semigroup. This dual method could be useful in finding a generalization to the case of a generalized free differential algebra, which may be relevant for physical applications in, e.g., higher-spin gauge theories.
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