Abstract
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.
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© 2010 Birkhäuser Verlag AG
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Ruzhansky, M., Turunen, V. (2010). Groups. In: Pseudo-Differential Operators and Symmetries. Pseudo-Differential Operators, vol 2. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8514-9_11
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DOI: https://doi.org/10.1007/978-3-7643-8514-9_11
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8513-2
Online ISBN: 978-3-7643-8514-9
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