Mirror geometry of lie algebras, lie groups, and homogeneous spaces

Book Cover
Publisher:
Kluwer Academic Publishers,
Pub. Date:
[2004]
Language:
English
Description
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.
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ISBN:
9781402025457
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Grouped Work ID720b9bdb-669e-a82d-fbbc-1a6d1cd24e06
Grouping Titlemirror geometry of lie algebras lie groups and homogeneous spaces
Grouping Authorsabinin lev v
Grouping Categorybook
Last Grouping Update2019-12-03 18:02:10PM
Last Indexed2019-12-14 03:31:35AM

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authorSabinin, Lev V. (Lev Vasilʹevitch)
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Bib IdFormatFormat CategoryEditionLanguagePublisherPublication DatePhysical Description
external_econtent:ils:.b29627369eBookeBookEnglishKluwer Academic Publishers, [2004]xvii, 312 pages : illustrations ; 25 cm.
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seriesMathematics and its applications
series_with_volumeMathematics and its applications|573
subject_facetElectronic books
Espaces homogènes
Homogeneous spaces
Lie algebras
Lie groups
Lie, Algèbres de
Lie, Groupes de
title_displayMirror geometry of lie algebras, lie groups, and homogeneous spaces
title_fullMirror geometry of lie algebras, lie groups, and homogeneous spaces [electronic resource] / by Lev V. Sabinin
title_shortMirror geometry of lie algebras, lie groups, and homogeneous spaces
topic_facetEspaces homogènes
Homogeneous spaces
Lie algebras
Lie groups
Lie, Algèbres de
Lie, Groupes de