关键词: 递归算法, 经典Maurer-Cartan算法, 活动标架, 微分不变量

Abstract: This paper presents a classical algorithm and an improved recursive method to construct moving frames and differential invariants based on the moving frame theory developed by Peter J. Olver and Mark Fels. It takes an example to demonstrate the constructive processes of two methods respectively for a Lie transformation group. The results indicate that the recursive algorithm has more advantages than the classical Maurer-Cartan approach, which can be applied to arbitrary group actions systematically. More importantly, it does not need the existing of a slice. Especially for multi-parameter transformation group, this recursive method is more convenient while constructing the corresponding moving frames and differential invariants. It is important that the corresponding Maurer-Cartan forms can be obtained as by-products step by step. The results presented here not only are new, but also provide a fundamental theory tool to the application study of signature curve for differential invariants.

Key words: recursive algorithm, classical Maurer-Cartan approach, moving frame, differential invariant