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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Arithmetik & Algebra Representation Theory of Finite Group Extensions
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Representation Theory of Finite Group Extensions
Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli (Broschiert, Englisch)
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Beschreibung
This monograph adopts an operational and functional analytic approach to the following problem: given a short exact sequence (group extension) 1 → N → G → H → 1 of finite groups, describe the irreducible representations of G by means of the structure of the group extension. This problem has attracted many mathematicians, including I. Schur, A.H. Clifford, and G. Mackey and, more recently, M.… Isaacs, B. Huppert, Y.G. Berkovich & E.M. Zhmud, and J.M.G. Fell & R.S. Doran. The main topics are, on the one hand, Clifford Theory and the Little Group Method (of Mackey and Wigner) for induced representations, and, on the other hand, Kirillov’s Orbit Method (for step-2 nilpotent groups of odd order) which establishes a natural and powerful correspondence between Lie rings and nilpotent groups. As an application, a detailed description is given of the representation theory of the alternating groups, of metacyclic, quaternionic, dihedral groups, and of the (finite) Heisenberg group. TheLittle Group Method may be applied if and only if a suitable unitary 2-cocycle (the Mackey obstruction) is trivial. To overcome this obstacle, (unitary) projective representations are introduced and corresponding Mackey and Clifford theories are developed. The commutant of an induced representation and the relative Hecke algebra is also examined. Finally, there is a comprehensive exposition of the theory of projective representations for finite Abelian groups which is applied to obtain a complete description of the irreducible representations of finite metabelian groups of odd order. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
30.11.2023
Sprache
Englisch
EAN
9783031138751
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Springer Monographs in Mathematics
Sonderedition
Nein
Autor
Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli
Seitenanzahl
340
Einbandart
Broschiert
Buch Untertitel
Clifford Theory, Mackey Obstruction, and the Orbit Method
Schlagwörter
Induced representation, Unitary Representation, Projective Representation, Orbit Method, Mackey Obstruction, Metabelian Group, Cohomology of Groups, Character Theory, Finite Group, Group Extension, Clifford Theory, Mackey Theory, Nilpotent Group, Heisenberg Group, Little Group Method, Hecke Algebra, Lie Ring, Schur Multiplier, Unitary 2-cocycle, Central Group Extension
Thema-Inhalt
PBG - Gruppen und Gruppentheorie
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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