Vorlesung: Gruppentheorie in Molekül - KFU

P.Knoll, Gruppentheorie in Molekül- und Festkörperphysik Seite 120
Def. 1.4: Farbsymmetrie..........................................................................................................14
Def. 1.5: Asymmetrie ..............................................................................................................16
Def. 2.1: Elemente...................................................................................................................22
Def. 2.2: Menge.......................................................................................................................22
Def. 2.3: Teilmenge.................................................................................................................22
Def. 2.4: Verknüpfung ............................................................................................................22
Def. 2.5: Gruppe......................................................................................................................22
Def. 2.6: Untergruppe..............................................................................................................23
Def. 2.7: Ordnung....................................................................................................................24
Def. 2.8: Klasseneinteilung .....................................................................................................24
Def. 2.9: abelsche Gruppen.....................................................................................................24
Def. 2.10: kommutative Elemente...........................................................................................24
Def. 2.11: Zentrum..................................................................................................................25
Def. 2.12: konjugierte Elemente .............................................................................................25
Def. 2.13: Nebenklassen..........................................................................................................25
Def. 2.14: Normalteiler ...........................................................................................................25
Def. 2.15: Faktorgruppe ..........................................................................................................25
Def. 2.16: Vektorraum (Tensorraum) .....................................................................................26
Def. 2.17: Unterraum ..............................................................................................................26
Def. 2.18: Inneres Produkt ......................................................................................................27
Def. 2.19: Gruppenalgebra......................................................................................................27
Def. 2.20: Idempotenz.............................................................................................................27
Def. 2.21: Direktes Produkt ⊗, Tensorprodukt.......................................................................27
Def. 2.22: Abbildung...............................................................................................................28
Def. 2.23: Äquivalenzrelation .................................................................................................28
Def. 2.24: Homomorphismus ..................................................................................................29
Def. 2.25: injektiv, Monomorphismus ....................................................................................29
Def. 2.26: surjektiv, Epimorphismus ......................................................................................29
Def. 2.27: bijektiv, Isomorphismus.........................................................................................29
Def. 2.28: Kern eines Homomorphismus................................................................................30
Def. 3.1: Symmetrieoperationen .............................................................................................31
Def. 3.2: Symmetrieelemente..................................................................................................32
Def. 3.3: Punktsymmetrien......................................................................................................32
Def. 3.4: Verknüpfung von Symmetrieoperationen................................................................32
Def. 4.1: linearer Operator ......................................................................................................43
Def. 4.2: Verknüpfungen von linearen Operatoren:................................................................43
Def. 4.3: G-Vektorraum: .........................................................................................................43
Def. 4.4: Darstellung ...............................................................................................................44
Def. 4.5: polarer Vektor ..........................................................................................................45
Def. 4.6: axialer Vektor...........................................................................................................45
Def. 4.7: eigentliche, uneigentliche Drehungen......................................................................45
Def. 4.8: Charakter..................................................................................................................46
Def. 4.9: reduzible Darstellung ...............................................................................................46
Def. 4.10: irreduzible Darstellung...........................................................................................46
Def. 4.11: G-invarianter Teilraum...........................................................................................46
Def. 4.12: Produkt von Darstellungen.....................................................................................48
Def. 4.13: Linearer Operator auf Tensorprodukt ....................................................................48
Def. 4.14: Symmetrisches und antisymmetrisches Tensorprodukt.........................................49
Def. 4.15: Zentrum der Gruppenalgebra .................................................................................49
Def. 4.16: Klassensumme........................................................................................................49
Def. 4.17: Orthogonalität in Gruppenalgebra .........................................................................50