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Mathematics - Algebra | p-Adic Lie Groups

p-Adic Lie Groups

Schneider, Peter

2011, XII, 256 p.

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  • First textbook with detailed exposition of Lazard's algebraic approach to compact p-adic Lie groups
  • Treats p-adic analysis in geometric language
  • Includes a chapter on locally convex topology on spaces of locally analytic functions
Manifolds over complete nonarchimedean fields together with notions like tangent spaces and vector fields form a convenient geometric language to express the basic formalism of p-adic analysis. The volume starts with a self-contained and detailed introduction to this language. This includes the discussion of spaces of locally analytic functions as topological vector spaces, important for applications in representation theory. 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. The second part of the book contains, for the first time in a textbook, a detailed exposition of Lazard's 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.

Content Level » Graduate

Keywords » 22E20, 16S34 - Lie group - completed group ring - locally analytic manifold - p-adic - p-valuation

Related subjects » Algebra

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