我们对具有三个自变量的超抛物型福克-普朗克方程进行了扩展对称性分析，该方程也称为柯尔莫哥洛夫方程，并因其卓越的对称性而在此类福克-普朗克方程中脱颖而出。特别是，其本质的李不变代数是八维的，这是上述类别中的最大维度。我们用直接法计算了福克-普朗克方程的完全点对称赝群，分析了它的结构并选出了它的本质子群。在列出该方程的本质和最大李不变代数的不等价一维和二维子代数之后，我们对其李约简进行了详尽的分类，执行其特殊的广义约简，并将后者的约简与通过李对称算子的迭代作用生成解相关联。因此，我们构造了一系列福克-普朗克方程的精确解，特别是那些由 (1+1) 维线性热方程的任意有限数量的任意解参数化的解。我们还建立了 Fokker-Planck 方程与 (1+2) 维 Kramers 方程的点相似性，该方程的基本李不变代数是八维的，这使我们能够以简单的方式找到这些 Kramers 方程的广泛精确解。方式。由 (1+1) 维线性热方程的任意有限数量的任意解参数化的那些。我们还建立了 Fokker-Planck 方程与 (1+2) 维 Kramers 方程的点相似性，该方程的基本李不变代数是八维的，这使我们能够以简单的方式找到这些 Kramers 方程的广泛精确解。方式。由 (1+1) 维线性热方程的任意有限数量的任意解参数化的那些。我们还建立了 Fokker-Planck 方程与 (1+2) 维 Kramers 方程的点相似性，该方程的基本李不变代数是八维的，这使我们能够以简单的方式找到这些 Kramers 方程的广泛精确解。方式。

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We carry out the extended symmetry analysis of an ultraparabolic Fokker–Planck equation with three independent variables, which is also called the Kolmogorov equation and is singled out within the class of such Fokker–Planck equations by its remarkable symmetry properties. In particular, its essential Lie invariance algebra is eight-dimensional, which is the maximum dimension within the above class. We compute the complete point symmetry pseudogroup of the Fokker–Planck equation using the direct method, analyse its structure and single out its essential subgroup. After listing inequivalent one- and two-dimensional subalgebras of the essential and maximal Lie invariance algebras of this equation, we exhaustively classify its Lie reductions, carry out its peculiar generalised reductions and relate the latter reductions to generating solutions with iterative action of Lie-symmetry operators. As a result, we construct wide families of exact solutions of the Fokker–Planck equation, in particular, those parameterised by an arbitrary finite number of arbitrary solutions of the (1+1)-dimensional linear heat equation. We also establish the point similarity of the Fokker–Planck equation to the (1+2)-dimensional Kramers equations whose essential Lie invariance algebras are eight-dimensional, which allows us to find wide families of exact solutions of these Kramers equations in an easy way.