标题： 爱因斯坦真空方程在N维中的李对称性 显示英文标题

标题： Lie Symmetries of Einstein's Vacuum Equations in N Dimensions

摘要： 我们研究了N维爱因斯坦真空方程（带有宇宙学项）的李对称性。 为此，我们首先写出生成对称性的向量场的二阶延拓，并计算其在爱因斯坦方程上的作用。 而不是将所有独立偏导数的系数设为零（这涉及爱因斯坦方程的非常复杂的替换），我们将那些在爱因斯坦方程中不出现的导数的系数设为零。 这大大限制了生成对称性的向量场的系数。 利用对称性生成元的李代数性质以及一般坐标变换是爱因斯坦方程的对称性这一事实，我们能够得到所有的李对称性。 我们使用的方法可能可以应用于其他类型的方程。 显示英文摘要

摘要： We investigate Lie symmetries of Einstein's vacuum equations in N dimensions, with a cosmological term. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on Einstein's equations. Instead of setting to zero the coefficients of all independent partial derivatives (which involves a very complicated substitution of Einstein's equations), we set to zero the coefficients of derivatives that do not appear in Einstein's equations. This considerably constrains the coefficients of symmetry generating vector fields. Using the Lie algebra property of generators of symmetries and the fact that general coordinate transformations are symmetries of Einstein's equations, we are then able to obtain all the Lie symmetries. The method we have used can likely be applied to other types of equations.