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Though the theory of p adic lie groups is now well grounded and to some extent unified with traditional lie group theory it remains at some distance from linear algebraic groups. The author then sets up the analytic foundations of the theory of p adic lie groups and develops the relation between p adic lie groups and their lie algebras.

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In rough terms a lie group is a continuous group that is one whose elements are described by several real parameters.

Padic Lie Groups Book Depository. The first based on a graduate course schneider teaches at münster gives a p adic analytic account of the theory which is much like the classical theory of lie groups. Lie groups and lie algebras addison wesley 1975 translated from french 2 j p. A p adic lie group is a locally analytic manifold over a non archimedean field that has a locally analytic group structure.

The second part of the book contains for the first time in a textbook a detailed exposition of lazards algebraic approach to compact p adic lie groups via his notion of a p valuation together with its application to the structure of completed group rings. As such lie groups provide a natural model for the concept of continuous symmetry such as rotational sy. Lie groups are named after norwegian mathematician sophus lie who laid the foundations of the theory of continuous transformation groups.

Serre lie algebras and lie groups benjamin 1965 translated from french. The notion of a p adic lie group has been around for a while but they have recently become more prominent in number theory and representation theory. In mathematics a lie group is a group that is also a differentiable manifold with the property that the group operations are smooth.

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