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

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Published:
Dordrecht ; Boston : Kluwer Academic Publishers, [2004].
Format:
ISBN:
9781402025457, 1402025459
Content Description:
xvii, 312 pages : illustrations ; 25 cm.
Status:
Available Online
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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APA Citation (style guide)

Sabinin, L. V. (2004). Mirror geometry of lie algebras, lie groups, and homogeneous spaces. Dordrecht ; Boston: Kluwer Academic Publishers.

Chicago / Turabian - Author Date Citation (style guide)

Sabinin, Lev V. 2004. Mirror Geometry of Lie Algebras, Lie Groups, and Homogeneous Spaces. Dordrecht ; Boston: Kluwer Academic Publishers.

Chicago / Turabian - Humanities Citation (style guide)

Sabinin, Lev V, Mirror Geometry of Lie Algebras, Lie Groups, and Homogeneous Spaces. Dordrecht ; Boston: Kluwer Academic Publishers, 2004.

MLA Citation (style guide)

Sabinin, Lev V. Mirror Geometry of Lie Algebras, Lie Groups, and Homogeneous Spaces. Dordrecht ; Boston: Kluwer Academic Publishers, 2004.

Note! Citation formats are based on standards as of July 2010. Citations contain only title, author, edition, publisher, and year published. Citations should be used as a guideline and should be double checked for accuracy.
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Language:
English

Notes

Bibliography
Includes bibliographical references (pages 305-308) and index.
Reproduction
Electronic reproduction.,New York :,Springer,,2008.,Mode of access: World Wide Web.,System requirements: Web browser.,Title from title screen (viewed on Oct. 10, 2008).,Access may be restricted to users at subscribing institutions.
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Last Sierra Extract TimeDec 03, 2019 06:02:01 PM
Last File Modification TimeDec 17, 2019 03:33:02 AM
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