| 书目名称 | Mirror Geometry of Lie Algebras, Lie Groups and Homogeneous Spaces | | 编辑 | Lev V. Sabinin | | 视频video | | | 丛书名称 | Mathematics and Its Applications | | 图书封面 |  | | 描述 | 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 algebr | | 出版日期 | Book 2004 | | 关键词 | Lie algebra; Lie group; Riemannian manifold; brandonwiskunde; curvature; differential geometry | | 版次 | 1 | | doi | https://doi.org/10.1007/1-4020-2545-9 | | isbn_softcover | 978-90-481-6676-3 | | isbn_ebook | 978-1-4020-2545-7 | | copyright | Springer Science+Business Media B.V. 2004 |
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发表于 2025-3-21 16:43:48
