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• W2785463906 abstract "The third chapter provides a historical survey of the theory of infinite continuous groups, a notion which Lie first introduced as a generalization of the classical notion of a finite continuous group. Contrary to its finite counterpart, an infinite continuous group does not admit any finite parameterization and can only be characterized in terms of a system of partial differential equations whose solutions represent the transformations of the group itself. Nowadays, infinite continuous groups are usually referred to as Lie pseudogroups of infinite type. Starting from Lie's pioneering works dating back to the early 1880s, we describe the subsequent developments up to Vessiot's monumental Memoire couronnee . We provide a discussion of the generalization of three fundamental theorems of classical Lie theory to infinite-dimensional domains by pointing out the difficulty the Lie approach had to face. Beyond preparing the ground for the next chapters by providing a detailed contextualization of Cartan theory, the aim is to contribute to a more accurate historical understanding of Lie theory of transformation groups too." @default.
• W2785463906 created "2018-02-23" @default.
• W2785463906 creator A5019752885 @default.
• W2785463906 date "2018-01-01" @default.
• W2785463906 modified "2023-09-26" @default.
• W2785463906 title "Infinite Continuous Groups 1883–1902 * *This chapter is partially based on (Cogliati, 2014)." @default.
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• W2785463906 doi "https://doi.org/10.1016/b978-0-12-814244-8.00003-6" @default.
• W2785463906 hasPublicationYear "2018" @default.
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