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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Geometrie Mirror Geometry of Lie Algebras, Lie Groups and Homogeneous Spaces
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Mirror Geometry of Lie Algebras, Lie Groups and Homogeneous Spaces
Lev V. Sabinin (Taschenbuch, Englisch)
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Beschreibung
As K. Nomizu has justly noted [K. Nomizu, 56], Differential Geometry ever will be initiating newer and newer aspects of the theory of Lie groups. This monograph is devoted to just some such aspects of Lie groups and Lie algebras. New differential geometric problems came into being in connection with so called subsymmetric spaces, subsymmetries, and mirrors introduced in our works dating back to… 1957 [L.V. Sabinin, 58a,59a,59b]. In addition, the exploration of mirrors and systems of mirrors is of interest in the case of symmetric spaces. Geometrically, the most rich in content there appeared to be the homogeneous Riemannian spaces with systems of mirrors generated by commuting subsymmetries, in particular, so called tri-symmetric spaces introduced in [L.V. Sabinin, 61b]. As to the concrete geometric problem which needs be solved and which is solved in this monograph, we indicate, for example, the problem of the classification of all tri-symmetric spaces with simple compact groups of motions. Passing from groups and subgroups connected with mirrors and subsymmetries to the corresponding Lie algebras and subalgebras leads to an important new concept of the involutive sum of Lie algebras [L.V. Sabinin, 65]. This concept is directly concerned with unitary symmetry of elementary par- cles (see [L.V. Sabinin, 95,85] and Appendix 1). The first examples of involutive (even iso-involutive) sums appeared in the - ploration of homogeneous Riemannian spaces with and axial symmetry. The consideration of spaces with mirrors [L.V. Sabinin, 59b] again led to iso-involutive sums. 53,49 €
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Technische Daten
Erscheinungsdatum
28.10.2010
Sprache
Englisch
EAN
9789048166763, 9789048166763
Herausgeber
Springer Netherland
Serien- oder Bandtitel
Mathematics and Its Applications
Sonderedition
Nein
Autor
Lev V. Sabinin
Seitenanzahl
312
Einbandart
Taschenbuch
Schlagwörter
Lie algebra, Lie group, Riemannian manifold, brandonwiskunde, curvature, differential geometry
Thema-Inhalt
PBM - Geometrie
PBMP - Differentielle und Riemannsche Geometrie
PBG - Gruppen und Gruppentheorie
Höhe
240 mm
Breite
16 cm
Transparenz & Sicherheit
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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