2010 | OriginalPaper | Buchkapitel
Groups
verfasst von : Michael Ruzhansky, Ville Turunen
Erschienen in: Pseudo-Differential Operators and Symmetries
Verlag: Birkhäuser Basel
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Loosely speaking, groups encode symmetries of (geometric) objects: if we consider a space
X
with some specific structure (e.g., a Riemannian manifold), a
symmetry of X
is a bijection
f: X→X
preserving the natural involved structure (e.g., the Riemannian metric) — here, the compositions and inversions of symmetries yield new symmetries. In a handful of assumptions, the concept of groups captures the essential properties of wide classes of symmetries, and provides powerful tools for related analysis.