Reductive homogeneous spaces of the compact Lie group \(G_2\). (English) Zbl 1537.22050
Albuquerque, Helena (ed.) et al., Non-associative algebras and related topics. NAART II. Selected papers based on the presentations at the 2nd conference, Coimbra, Portugal, July 18–22, 2022. Cham: Springer. Springer Proc. Math. Stat. 427, 29-63 (2023).
Summary: The first author defended her doctoral thesis [Espacios homogéneos reductivos y álgebras no asociativas. La Rioja: Universidad de La Rioja (PhD Thesis) (2001)] in 2001, supervised by P. Benito and A. Elduque. This thesis contained the classification of the Lie-Yamaguti algebras with standard enveloping algebra \(\mathfrak{g}_2\) over fields of characteristic zero, which in particular gives the classification of the homogeneous reductive spaces of the compact Lie group \(G_2\). In this work we revisit this classification from a more geometrical approach. We provide too geometric models of the corresponding homogeneous spaces and make explicit some relations among them.
For the entire collection see [Zbl 1531.17001].
For the entire collection see [Zbl 1531.17001].
MSC:
| 22F30 | Homogeneous spaces |
| 17B25 | Exceptional (super)algebras |
| 53C30 | Differential geometry of homogeneous manifolds |
Keywords:
octonions; exceptional algebra \(\mathfrak{g}_2\); exceptional group \(G_2\); homogeneous manifoldReferences:
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